Internal problem ID [1188]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y+2 x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=-2*x^2,y(1) = 1, D(y)(1) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {-x^{4}+2 x^{3}+1}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 21
DSolve[{x^2*y''[x]+2*x*y'[x]-2*y[x]==-2*x^2,{y[1]==1,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{2}+\frac {1}{2 x^2}+x \\ \end{align*}