Sr Examen
Ecuación diferencial 4y'''+y''-2y'-y=2*e^2
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Solución
Ha introducido
[src]
3 2
d d d 2
-y(x) - 2*--(y(x)) + 4*---(y(x)) + ---(y(x)) = 2*e
dx 3 2
dx dx
$$- y{\left(x \right)} - 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 4 \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 2 e^{2}$$
-y - 2*y' + y'' + 4*y''' = 2*exp(2)
Respuesta
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/ __________________ \ / __________________ \ / __________________ \
| 3 / _____ 25 | | 3 / _____ 25 | | 3 / _____ 25 |
x*|-1 + \/ 179 + 12*\/ 114 + ---------------------| x*|-2 - \/ 179 + 12*\/ 114 - ---------------------| / / __________________ \\ / / __________________ \\ x*|-2 - \/ 179 + 12*\/ 114 - ---------------------|
| __________________| | __________________| | ___ | 3 / _____ 25 || | ___ | 3 / _____ 25 || | __________________|
| 3 / _____ | | 3 / _____ | |x*\/ 3 *|- \/ 179 + 12*\/ 114 + ---------------------|| |x*\/ 3 *|- \/ 179 + 12*\/ 114 + ---------------------|| | 3 / _____ |
\ \/ 179 + 12*\/ 114 / \ \/ 179 + 12*\/ 114 / | | __________________|| | | __________________|| \ \/ 179 + 12*\/ 114 /
------------------------------------------------------ ------------------------------------------------------ | | 3 / _____ || | | 3 / _____ || ------------------------------------------------------
2 12 24 | \ \/ 179 + 12*\/ 114 /| | \ \/ 179 + 12*\/ 114 /| 24
y(x) = - 2*e + C3*e + C1*e *sin|---------------------------------------------------------| + C2*cos|---------------------------------------------------------|*e
\ 24 / \ 24 /
$$y{\left(x \right)} = C_{1} e^{\frac{x \left(- \sqrt[3]{12 \sqrt{114} + 179} - \frac{25}{\sqrt[3]{12 \sqrt{114} + 179}} - 2\right)}{24}} \sin{\left(\frac{\sqrt{3} x \left(- \sqrt[3]{12 \sqrt{114} + 179} + \frac{25}{\sqrt[3]{12 \sqrt{114} + 179}}\right)}{24} \right)} + C_{2} e^{\frac{x \left(- \sqrt[3]{12 \sqrt{114} + 179} - \frac{25}{\sqrt[3]{12 \sqrt{114} + 179}} - 2\right)}{24}} \cos{\left(\frac{\sqrt{3} x \left(- \sqrt[3]{12 \sqrt{114} + 179} + \frac{25}{\sqrt[3]{12 \sqrt{114} + 179}}\right)}{24} \right)} + C_{3} e^{\frac{x \left(-1 + \frac{25}{\sqrt[3]{12 \sqrt{114} + 179}} + \sqrt[3]{12 \sqrt{114} + 179}\right)}{12}} - 2 e^{2}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral