Internal problem ID [257]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 62.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y-x^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve((x^2-1)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=x^2-1,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +\left (x^{2}+1\right ) c_{1}+\frac {\left (x -1\right )^{2} \ln \left (x -1\right )}{2}+\frac {\left (x +1\right )^{2} \ln \left (x +1\right )}{2}-x^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (x \log (x)+(-1+c_2) x+c_1) \\ \end{align*}