Internal problem ID [2014]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve((x+1)^2*diff(y(x),x$2)+3*(x+1)*diff(y(x),x)+y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x +1\right ) c_{1}}{x +1}+\frac {c_{2}}{x +1}-\frac {-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )-6 x}{18 \left (x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 42
DSolve[(x+1)^2*y''[x]+3*(x+1)*y'[x]+y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (x (2 x-3)+6)+6 (-1+3 c_2) \log (x+1)+18 c_1}{18 (x+1)} \\ \end{align*}