Sr Examen
Ecuación diferencial y''''''-8y'''=1+4x*sin(x*3^(1/2))*e^(-2x)+sin(2x)*x^(2)*e^(x)
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Solución
Ha introducido
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3 6
d d 2 x -2*x / ___\
- 8*---(y(x)) + ---(y(x)) = 1 + x *e *sin(2*x) + 4*x*e *sin\x*\/ 3 /
3 6
dx dx
$$- 8 \frac{d^{3}}{d x^{3}} y{\left(x \right)} + \frac{d^{6}}{d x^{6}} y{\left(x \right)} = x^{2} e^{x} \sin{\left(2 x \right)} + 4 x e^{- 2 x} \sin{\left(\sqrt{3} x \right)} + 1$$
-8*y''' + y'''''' = x^2*exp(x)*sin(2*x) + 4*x*exp(-2*x)*sin(sqrt(3)*x) + 1
Respuesta
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3 / / / ___\ ___ / ___\\ -2*x x\ / x\ x / / ___\ ___ / ___\\ -2*x
x 2*x | 4*\- 223*sin\x*\/ 3 / - 108*\/ 3 *cos\x*\/ 3 //*e 12*(-1133*sin(2*x) + 5406*cos(2*x))*e | 2 | (-12*cos(2*x) + 41*sin(2*x))*e | / / ___\ / ___\\ -x 6*(-3647293*sin(2*x) - 3073024*cos(2*x))*e 72*\- 26174*sin\x*\/ 3 / - 35851*\/ 3 *cos\x*\/ 3 //*e
y(x) = C1 - -- + C6*e + x*|C2 + ----------------------------------------------------- + --------------------------------------| + x *|C3 + -------------------------------| + \C4*sin\x*\/ 3 / + C5*cos\x*\/ 3 //*e + ------------------------------------------- + ----------------------------------------------------------
48 \ 84721 3330625 / \ 9125 / 1215678125 146482609
$$y{\left(x \right)} = C_{1} + C_{6} e^{2 x} - \frac{x^{3}}{48} + x^{2} \left(C_{3} + \frac{\left(41 \sin{\left(2 x \right)} - 12 \cos{\left(2 x \right)}\right) e^{x}}{9125}\right) + x \left(C_{2} + \frac{12 \left(- 1133 \sin{\left(2 x \right)} + 5406 \cos{\left(2 x \right)}\right) e^{x}}{3330625} + \frac{4 \left(- 223 \sin{\left(\sqrt{3} x \right)} - 108 \sqrt{3} \cos{\left(\sqrt{3} x \right)}\right) e^{- 2 x}}{84721}\right) + \left(C_{4} \sin{\left(\sqrt{3} x \right)} + C_{5} \cos{\left(\sqrt{3} x \right)}\right) e^{- x} + \frac{6 \left(- 3647293 \sin{\left(2 x \right)} - 3073024 \cos{\left(2 x \right)}\right) e^{x}}{1215678125} + \frac{72 \left(- 26174 \sin{\left(\sqrt{3} x \right)} - 35851 \sqrt{3} \cos{\left(\sqrt{3} x \right)}\right) e^{- 2 x}}{146482609}$$
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