Internal problem ID [5071]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number: 3.
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 }+x y^{\prime }-y-x^{2}-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=x^2+2*x,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+c_{2} x +\frac {\left (x +3 \ln \relax (x )\right ) x}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[x^2*y''[x]+x*y'[x]-y[x]==x^2+2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{3}+x \log (x)+\left (-\frac {1}{2}+c_2\right ) x+\frac {c_1}{x} \\ \end{align*}