Internal problem ID [6361]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 70.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {a y y^{\prime \prime }+b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 22
dsolve(a*y(x)*diff(y(x),x$2)+b*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -\frac {b \,x^{2}}{2 a}+c_{1} x +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 28
DSolve[a*y[x]*y''[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to -\frac {b x^2}{2 a}+c_2 x+c_1 \\ \end{align*}