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-
¿Cómo usar?
- Ecuación diferencial:
- Ecuación -3*x^2*y+y'=x^2
- Ecuación 3*x^2*y'=4*x^2+8*x*y+y^2
- Ecuación 2yy'=1
- Ecuación y''+y=4*e^x
- Integral de d{x}:
- 2e^x
- Derivada de:
-
2e^x
-
Expresiones idénticas
- y4y'''+y''-2y'-y=2e^x
- y4y derivada de tercer (3) orden más y dos signos de prima para el segundo (2) orden menos 2y signo de prima para el primer (1) orden menos y es igual a 2e en el grado x
- y4y'''+y''-2y'-y=2ex
-
Expresiones semejantes
- y4y'''+y''+2y'-y=2e^x
- y4y'''+y''-2y'+y=2e^x
- y4y'''-y''-2y'-y=2e^x
Ecuación diferencial y4y'''+y''-2y'-y=2e^x
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
3 2
d d d x
-y(x) - 2*--(y(x)) + y4*---(y(x)) + ---(y(x)) = 2*e
dx 3 2
dx dx
$$y_{4} \frac{d^{3}}{d x^{3}} y{\left(x \right)} - y{\left(x \right)} - 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 2 e^{x}$$
y4*y''' - y - 2*y' + y'' = 2*exp(x)
Respuesta
[src]
/ _________________________________________________________________ \ / _________________________________________________________________ _________________________________________________________________\ / _________________________________________________________________ _________________________________________________________________\
| / _________________________________ | | / _________________________________ / _________________________________ | | / _________________________________ / _________________________________ |
| / / 3 | | / / 3 / / 3 | | / / 3 / / 3 |
| / / / 1 \ | | / / / 1 \ / / / 1 \ | | / / / 1 \ / / / 1 \ |
| / / 2 4*|6 + --| | | / / 2 4*|6 + --| / / 2 4*|6 + --| | | / / 2 4*|6 + --| / / 2 4*|6 + --| |
| / / / 2 18\ \ y4/ | | / / / 2 18\ \ y4/ / / / 2 18\ \ y4/ | | / / / 2 18\ \ y4/ / / / 2 18\ \ y4/ |
| / / |-27 + --- + --| - ----------- | | / / |-27 + --- + --| - ----------- / / |-27 + --- + --| - ----------- | | / / |-27 + --- + --| - ----------- / / |-27 + --- + --| - ----------- |
| / / | 2 y4| y4 | | / / | 2 y4| y4 / / | 2 y4| y4 | | / / | 2 y4| y4 / / | 2 y4| y4 |
| / / \ y4 / | | / / \ y4 / / / \ y4 / | | / / \ y4 / / / \ y4 / |
| / / ------------------------------- | | / / ------------------------------- / / ------------------------------- | | / / ------------------------------- / / ------------------------------- |
| / / 2 | | / / 2 / / 2 | | / / 2 / / 2 |
| / 1 \/ y4 9 27 | | / 1 \/ y4 9 27 ___ / 1 \/ y4 9 27 | | / 1 \/ y4 9 27 ___ / 1 \/ y4 9 27 |
| / --- + -------------------------------------------- + --- - ---- | | / --- + -------------------------------------------- + --- - ---- I*\/ 3 * / --- + -------------------------------------------- + --- - ---- | | / --- + -------------------------------------------- + --- - ---- I*\/ 3 * / --- + -------------------------------------------- + --- - ---- |
| 3 / 3 2 2 2*y4 | | 3 / 3 2 2 2*y4 3 / 3 2 2 2*y4 | | 3 / 3 2 2 2*y4 3 / 3 2 2 2*y4 |
| 1 \/ y4 y4 2 1 | | 1 \/ y4 y4 4 2 \/ y4 y4 | | 1 \/ y4 y4 4 2 \/ y4 y4 |
x*|- ---- - -------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------| x*|- ---- + -------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------| x*|- ---- + -------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------|
| 3*y4 3 _________________________________________________________________ _________________________________________________________________| | 3*y4 6 _________________________________________________________________ _________________________________________________________________ 6 | | 3*y4 6 _________________________________________________________________ _________________________________________________________________ 6 |
| / _________________________________ / _________________________________ | | / _________________________________ / _________________________________ | | / _________________________________ / _________________________________ |
| / / 3 / / 3 | | / / 3 / / 3 | | / / 3 / / 3 |
| / / / 1 \ / / / 1 \ | | / / / 1 \ / / / 1 \ | | / / / 1 \ / / / 1 \ |
| / / 2 4*|6 + --| / / 2 4*|6 + --| | | / / 2 4*|6 + --| / / 2 4*|6 + --| | | / / 2 4*|6 + --| / / 2 4*|6 + --| |
| / / / 2 18\ \ y4/ / / / 2 18\ \ y4/ | | / / / 2 18\ \ y4/ / / / 2 18\ \ y4/ | | / / / 2 18\ \ y4/ / / / 2 18\ \ y4/ |
| / / |-27 + --- + --| - ----------- / / |-27 + --- + --| - ----------- | | / / |-27 + --- + --| - ----------- / / |-27 + --- + --| - ----------- | | / / |-27 + --- + --| - ----------- / / |-27 + --- + --| - ----------- |
| / / | 2 y4| y4 / / | 2 y4| y4 | | / / | 2 y4| y4 / / | 2 y4| y4 | | / / | 2 y4| y4 / / | 2 y4| y4 |
| / / \ y4 / / / \ y4 / | | / / \ y4 / / / \ y4 / | | / / \ y4 / / / \ y4 / |
| / / ------------------------------- / / ------------------------------- | | / / ------------------------------- / / ------------------------------- | | / / ------------------------------- / / ------------------------------- |
| / / 2 / / 2 | | / / 2 / / 2 | | / / 2 / / 2 |
| / 1 \/ y4 9 27 2 / 1 \/ y4 9 27 | | / ___\ / 1 \/ y4 9 27 2 / ___\ / 1 \/ y4 9 27 | | / ___\ / 1 \/ y4 9 27 2 / ___\ / 1 \/ y4 9 27 |
| y4* / --- + -------------------------------------------- + --- - ---- 3*y4 * / --- + -------------------------------------------- + --- - ---- | | y4*\-1 + I*\/ 3 /* / --- + -------------------------------------------- + --- - ---- 3*y4 *\-1 + I*\/ 3 /* / --- + -------------------------------------------- + --- - ---- | | y4*\-1 - I*\/ 3 /* / --- + -------------------------------------------- + --- - ---- 3*y4 *\-1 - I*\/ 3 /* / --- + -------------------------------------------- + --- - ---- |
| 3 / 3 2 2 2*y4 3 / 3 2 2 2*y4 | | 3 / 3 2 2 2*y4 3 / 3 2 2 2*y4 | | 3 / 3 2 2 2*y4 3 / 3 2 2 2*y4 | x
\ \/ y4 y4 \/ y4 y4 / \ \/ y4 y4 \/ y4 y4 / \ \/ y4 y4 \/ y4 y4 / 2*e
y(x) = C1*e + C2*e + C3*e + -------
-2 + y4
$$y{\left(x \right)} = C_{1} e^{x \left(- \frac{\sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}{3} - \frac{1}{3 y_{4}} - \frac{2}{y_{4} \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}} - \frac{1}{3 y_{4}^{2} \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}\right)} + C_{2} e^{x \left(\frac{\sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}{6} - \frac{\sqrt{3} i \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}{6} - \frac{1}{3 y_{4}} - \frac{4}{y_{4} \left(-1 + \sqrt{3} i\right) \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}} - \frac{2}{3 y_{4}^{2} \left(-1 + \sqrt{3} i\right) \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}\right)} + C_{3} e^{x \left(\frac{\sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}{6} + \frac{\sqrt{3} i \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}{6} - \frac{1}{3 y_{4}} - \frac{4}{y_{4} \left(-1 - \sqrt{3} i\right) \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}} - \frac{2}{3 y_{4}^{2} \left(-1 - \sqrt{3} i\right) \sqrt[3]{\frac{\sqrt{\frac{\left(-27 + \frac{18}{y_{4}} + \frac{2}{y_{4}^{2}}\right)^{2} - \frac{4 \left(6 + \frac{1}{y_{4}}\right)^{3}}{y_{4}}}{y_{4}^{2}}}}{2} - \frac{27}{2 y_{4}} + \frac{9}{y_{4}^{2}} + \frac{1}{y_{4}^{3}}}}\right)} + \frac{2 e^{x}}{y_{4} - 2}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral