Internal problem ID [11824]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 50.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }=x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 91
dsolve(diff(y(x),x$6)+2*diff(y(x),x$5)+5*diff(y(x),x$4)=x^3+x^2*exp(-x)+exp(-x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{5} x +c_{6} +\frac {\left (\int \left (\left (\left (-330 x +1320 c_{1} +240 c_{2} +69\right ) \cos \left (2 x \right )+\left (60 x -240 c_{1} +1320 c_{2} +567\right ) \sin \left (2 x \right )-3750 x^{2}-22500 x -43125\right ) {\mathrm e}^{-x}+25 x^{6}-60 x^{5}-30 x^{4}+288 x^{3}+7500 c_{3} x^{2}+15000 c_{4} x \right )d x \right )}{15000} \]
✓ Solution by Mathematica
Time used: 11.809 (sec). Leaf size: 119
DSolve[y''''''[x]+2*y'''''[x]+5*y''''[x]==x^3+x^2*Exp[-x]+Exp[-x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_6 x^3+c_5 x^2+\frac {e^{-x} \left (10 \left (25 e^x x^7-70 e^x x^6-42 e^x x^5+504 e^x x^4+26250 x^2+210000 x+511875\right )+84 (35 x-2 (97+240 c_1+70 c_2)) \cos (2 x)-21 (480 x+643+560 c_1-1920 c_2) \sin (2 x)\right )}{1050000}+c_4 x+c_3 \]