Internal problem ID [11849]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y=\left (x +2\right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve((x^2+2*x)*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=(x+2)^2,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (x \right ) x^{2}+\left (c_{2} -1\right ) x^{2}+\left (-2+c_{1} \right ) x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 31
DSolve[(x^2+2*x)*y''[x]-2*(x+1)*y'[x]+2*y[x]==(x+2)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \log (x)+(-1+c_1) x^2-(2+c_2) x-c_2 \]