Internal problem ID [1172]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }-4 y x^{3}-8 x^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 22
dsolve(x*diff(y(x),x$2)-diff(y(x),x)-4*x^3*y(x)=8*x^5,y(x), singsol=all)
\[ y \relax (x ) = \sinh \left (x^{2}\right ) c_{2}+\cosh \left (x^{2}\right ) c_{1}-2 x^{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 28
DSolve[x*y''[x]-y'[x]-4*x^3*y[x]==8*x^5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x^2+c_1 \cosh \left (x^2\right )+i c_2 \sinh \left (x^2\right ) \\ \end{align*}