Sr Examen
Ecuación diferencial y'''-3y''-4y'-12y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 3
d d d
-12*y(x) - 4*--(y(x)) - 3*---(y(x)) + ---(y(x)) = 0
dx 2 3
dx dx
$$- 12 y{\left(x \right)} - 4 \frac{d}{d x} y{\left(x \right)} - 3 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$$
-12*y - 4*y' - 3*y'' + y''' = 0
Respuesta
[src]
/ ________________\ / ________________\
| / ______ | | / ______ |
/ ________________ \ | / 2*\/ 1383 | / / ________________ \\ / / ________________ \\ | / 2*\/ 1383 |
| / ______ | | 3 / 9 + ---------- | | | / ______ || | | / ______ || | 3 / 9 + ---------- |
| / 2*\/ 1383 7 | | 7 \/ 9 | | ___ | / 2*\/ 1383 7 || | ___ | / 2*\/ 1383 7 || | 7 \/ 9 |
x*|1 + 3 / 9 + ---------- + -----------------------| x*|1 - ----------------------- - ---------------------| |x*\/ 3 *|- 3*3 / 9 + ---------- + ---------------------|| |x*\/ 3 *|- 3*3 / 9 + ---------- + ---------------------|| x*|1 - ----------------------- - ---------------------|
| \/ 9 ________________| | ________________ 2 | | | \/ 9 ________________|| | | \/ 9 ________________|| | ________________ 2 |
| / ______ | | / ______ | | | / ______ || | | / ______ || | / ______ |
| / 2*\/ 1383 | | / 2*\/ 1383 | | | / 2*\/ 1383 || | | / 2*\/ 1383 || | / 2*\/ 1383 |
| 3*3 / 9 + ---------- | | 6*3 / 9 + ---------- | | | 3 / 9 + ---------- || | | 3 / 9 + ---------- || | 6*3 / 9 + ---------- |
\ \/ 9 / \ \/ 9 / | \ \/ 9 /| | \ \/ 9 /| \ \/ 9 /
y(x) = C3*e + C1*e *sin|-----------------------------------------------------------| + C2*cos|-----------------------------------------------------------|*e
\ 6 / \ 6 /
$$y{\left(x \right)} = C_{1} e^{x \left(- \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1\right)} \sin{\left(\frac{\sqrt{3} x \left(- 3 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9} + \frac{7}{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}\right)}{6} \right)} + C_{2} e^{x \left(- \frac{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}{2} - \frac{7}{6 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1\right)} \cos{\left(\frac{\sqrt{3} x \left(- 3 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9} + \frac{7}{\sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}}\right)}{6} \right)} + C_{3} e^{x \left(\frac{7}{3 \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}} + 1 + \sqrt[3]{\frac{2 \sqrt{1383}}{9} + 9}\right)}$$
Clasificación
nth linear constant coeff homogeneous