Internal problem ID [1161]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y-2 x^{2}-2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=2*x^2+2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +\frac {2 x^{2}}{3}+\frac {c_{1}}{x}-2 \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[x^2*y''[x]+x*y'[x]-y[x]==2*x^2+2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^2}{3}+c_2 x+\frac {c_1}{x}-2 \\ \end{align*}