56.1.70 problem 70

Internal problem ID [8782]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 70
Date solved : Monday, January 27, 2025 at 04:58:31 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} a y y^{\prime \prime }+b y&=0 \end{align*}

✓ 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 &= 0 \\ y &= -\frac {b \,x^{2}}{2 a}+c_{1} x +c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

DSolve[a*y[x]*D[y[x],{x,2}]+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*}