56.1.65 problem 65

Internal problem ID [8777]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 65
Date solved : Monday, January 27, 2025 at 04:50:09 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{2} y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(y(x)^2*diff(y(x),x$2)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= c_{1} x +c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 17

DSolve[y[x]^2*D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ y(x)\to c_2 x+c_1 \\ \end{align*}