Sr Examen
Ecuación diferencial 2*y+2*y'+y'''=e^(-x)*x*cos(x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
3
d d -x
2*--(y(x)) + 2*y(x) + ---(y(x)) = x*cos(x)*e
dx 3
dx
$$2 y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = x e^{- x} \cos{\left(x \right)}$$
2*y + 2*y' + y''' = x*exp(-x)*cos(x)
Respuesta
[src]
/ _____________ 3 ___ \ / _____________ 3 ___ \ / _____________ 3 ___ \
3 ___ | 3 / _____ 2*\/ 3 | 3 ___ |3 / _____ 2*\/ 3 | 3 ___ |3 / _____ 2*\/ 3 |
x*\/ 3 *|- \/ 9 + \/ 105 + ----------------| x*\/ 3 *|\/ 9 + \/ 105 - ----------------| x*\/ 3 *|\/ 9 + \/ 105 - ----------------|
| _____________| | _____________| | _____________|
| 3 / _____ | | 3 / _____ | | 3 / _____ |
\ \/ 9 + \/ 105 / \ \/ 9 + \/ 105 / / / _____________\\ / / _____________\\ \ \/ 9 + \/ 105 /
----------------------------------------------- -x -x --------------------------------------------- | | 2/3 3 / _____ || | | 2/3 3 / _____ || --------------------------------------------- -x -x
3 e *sin(x) 3*cos(x)*e 6 | 6 ___ | 1 3 *\/ 9 + \/ 105 || | 6 ___ | 1 3 *\/ 9 + \/ 105 || 6 x*e *sin(x) x*cos(x)*e
y(x) = C3*e + ---------- + ------------ + C1*e *sin|x*\/ 3 *|---------------- + ---------------------|| + C2*cos|x*\/ 3 *|---------------- + ---------------------||*e + ------------ + ------------
10 10 | | _____________ 6 || | | _____________ 6 || 5 10
| |3 / _____ || | |3 / _____ ||
\ \\/ 9 + \/ 105 // \ \\/ 9 + \/ 105 //
$$y{\left(x \right)} = C_{1} e^{\frac{\sqrt[3]{3} x \left(- \frac{2 \sqrt[3]{3}}{\sqrt[3]{9 + \sqrt{105}}} + \sqrt[3]{9 + \sqrt{105}}\right)}{6}} \sin{\left(\sqrt[6]{3} x \left(\frac{1}{\sqrt[3]{9 + \sqrt{105}}} + \frac{3^{\frac{2}{3}} \sqrt[3]{9 + \sqrt{105}}}{6}\right) \right)} + C_{2} e^{\frac{\sqrt[3]{3} x \left(- \frac{2 \sqrt[3]{3}}{\sqrt[3]{9 + \sqrt{105}}} + \sqrt[3]{9 + \sqrt{105}}\right)}{6}} \cos{\left(\sqrt[6]{3} x \left(\frac{1}{\sqrt[3]{9 + \sqrt{105}}} + \frac{3^{\frac{2}{3}} \sqrt[3]{9 + \sqrt{105}}}{6}\right) \right)} + C_{3} e^{\frac{\sqrt[3]{3} x \left(- \sqrt[3]{9 + \sqrt{105}} + \frac{2 \sqrt[3]{3}}{\sqrt[3]{9 + \sqrt{105}}}\right)}{3}} + \frac{x e^{- x} \sin{\left(x \right)}}{5} + \frac{x e^{- x} \cos{\left(x \right)}}{10} + \frac{e^{- x} \sin{\left(x \right)}}{10} + \frac{3 e^{- x} \cos{\left(x \right)}}{10}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral