Internal problem ID [13222]
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: 14.2 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{-x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([(x+1)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,exp(-x)],y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 31
DSolve[(x+1)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 e c_2 x+c_1 \cosh (x)-c_1 \sinh (x)}{\sqrt {2 e}} \]