Internal problem ID [1176]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y-3 x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-(x^2-2)*y(x)=3*x^4,y(x), singsol=all)
\[ y \relax (x ) = x \sinh \relax (x ) c_{2}+x \cosh \relax (x ) c_{1}-3 x^{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 29
DSolve[x^2*y''[x]-2*x*y'[x]-(x^2-2)*y[x]==3*x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \left (-6 x+2 c_1 e^{-x}+c_2 e^x\right ) \\ \end{align*}