56.1.65 problem 65

Internal problem ID [8777]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 65
Date solved : Wednesday, March 05, 2025 at 06:47:44 AM
CAS classification : [[_2nd_order, _quadrature]]

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

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

ode:=y(x)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x \]