Sr Examen
Ecuación diferencial y'''+y''=3e^x+4x^2
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Solución
Ha introducido
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2 3 d d x 2 ---(y(x)) + ---(y(x)) = 3*e + 4*x 2 3 dx dx
$$\frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 4 x^{2} + 3 e^{x}$$
y'' + y''' = 4*x^2 + 3*exp(x)
Respuesta
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3 4 x
2 4*x x 3*e -x
y(x) = C1 + 4*x - ---- + -- + ---- + C2*x + C3*e
3 3 2
$$y{\left(x \right)} = C_{1} + C_{2} x + C_{3} e^{- x} + \frac{x^{4}}{3} - \frac{4 x^{3}}{3} + 4 x^{2} + \frac{3 e^{x}}{2}$$
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