Sr Examen
Ecuación diferencial y'''+5y''+3y'+9y=0
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Solución
Ha introducido
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2 3
d d d
3*--(y(x)) + 5*---(y(x)) + 9*y(x) + ---(y(x)) = 0
dx 2 3
dx dx
$$9 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + 5 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$$
9*y + 3*y' + 5*y'' + y''' = 0
Respuesta
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/ _________________ \ / _________________ \ / _________________ \
| 3 / _____ 16 | | 3 / _____ 16 | | 3 / _____ 16 |
x*|-5 - \/ 179 + 9*\/ 345 - --------------------| x*|-10 + \/ 179 + 9*\/ 345 + --------------------| / / _________________ \\ / / _________________ \\ x*|-10 + \/ 179 + 9*\/ 345 + --------------------|
| _________________| | _________________| | ___ | 3 / _____ 16 || | ___ | 3 / _____ 16 || | _________________|
| 3 / _____ | | 3 / _____ | |x*\/ 3 *|- \/ 179 + 9*\/ 345 + --------------------|| |x*\/ 3 *|- \/ 179 + 9*\/ 345 + --------------------|| | 3 / _____ |
\ \/ 179 + 9*\/ 345 / \ \/ 179 + 9*\/ 345 / | | _________________|| | | _________________|| \ \/ 179 + 9*\/ 345 /
---------------------------------------------------- ----------------------------------------------------- | | 3 / _____ || | | 3 / _____ || -----------------------------------------------------
3 6 | \ \/ 179 + 9*\/ 345 /| | \ \/ 179 + 9*\/ 345 /| 6
y(x) = C3*e + C1*e *sin|-------------------------------------------------------| + C2*cos|-------------------------------------------------------|*e
\ 6 / \ 6 /
$$y{\left(x \right)} = C_{1} e^{\frac{x \left(-10 + \frac{16}{\sqrt[3]{9 \sqrt{345} + 179}} + \sqrt[3]{9 \sqrt{345} + 179}\right)}{6}} \sin{\left(\frac{\sqrt{3} x \left(- \sqrt[3]{9 \sqrt{345} + 179} + \frac{16}{\sqrt[3]{9 \sqrt{345} + 179}}\right)}{6} \right)} + C_{2} e^{\frac{x \left(-10 + \frac{16}{\sqrt[3]{9 \sqrt{345} + 179}} + \sqrt[3]{9 \sqrt{345} + 179}\right)}{6}} \cos{\left(\frac{\sqrt{3} x \left(- \sqrt[3]{9 \sqrt{345} + 179} + \frac{16}{\sqrt[3]{9 \sqrt{345} + 179}}\right)}{6} \right)} + C_{3} e^{\frac{x \left(- \sqrt[3]{9 \sqrt{345} + 179} - 5 - \frac{16}{\sqrt[3]{9 \sqrt{345} + 179}}\right)}{3}}$$
Clasificación
nth linear constant coeff homogeneous