Internal problem ID [13790]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.1 (n).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y=\left (x +1\right )^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve((x+1)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=(x+1)^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x +c_{1} {\mathrm e}^{-x}+x^{2}+1 \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 41
DSolve[(x+1)*y''[x]+x*y'[x]-y[x]==(x+1)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+\left (-1+\sqrt {2 e} c_2\right ) x+\frac {c_1 e^{-x-\frac {1}{2}}}{\sqrt {2}}+1 \]