Sr Examen
Ecuación diferencial y'''-2y''+y'=(e^x)*cos(2x)+x*sin(x)+e^x+(1-x)*e^(x)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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2 3
d d d x x x
- 2*---(y(x)) + --(y(x)) + ---(y(x)) = x*sin(x) + (1 - x)*e + cos(2*x)*e + e
2 dx 3
dx dx
$$\frac{d}{d x} y{\left(x \right)} - 2 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = x \sin{\left(x \right)} + \left(1 - x\right) e^{x} + e^{x} \cos{\left(2 x \right)} + e^{x}$$
y' - 2*y'' + y''' = x*sin(x) + (1 - x)*exp(x) + exp(x)*cos(2*x) + exp(x)
Respuesta
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/ / 2 \\
sin(x) | sin(2*x) cos(2*x) | x 3*x|| x x*sin(x)
y(x) = C1 + ------ + |C2 - -------- - -------- + x*|C3 - -- + ---||*e + -------- + cos(x)
2 \ 10 20 \ 6 2 // 2
$$y{\left(x \right)} = C_{1} + \frac{x \sin{\left(x \right)}}{2} + \left(C_{2} + x \left(C_{3} - \frac{x^{2}}{6} + \frac{3 x}{2}\right) - \frac{\sin{\left(2 x \right)}}{10} - \frac{\cos{\left(2 x \right)}}{20}\right) e^{x} + \frac{\sin{\left(x \right)}}{2} + \cos{\left(x \right)}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral