Internal problem ID [13555]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.3 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y=\left (x +1\right )^{2}} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{-x} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([(x+1)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=(1+x)^2,exp(-x)],singsol=all)
\[ y \left (x \right ) = c_{2} x +c_{1} {\mathrm e}^{-x}+x^{2}+1 \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 41
DSolve[(x+1)*y''[x]+x*y'[x]-y[x]==(1+x)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+\left (-1+\sqrt {2 e} c_2\right ) x+\frac {c_1 e^{-x-\frac {1}{2}}}{\sqrt {2}}+1 \]