56.1.66 problem 66

Internal problem ID [8778]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 66
Date solved : Sunday, March 30, 2025 at 01:33:00 PM
CAS classification : [NONE]

\begin{align*} 3 y y^{\prime \prime }&=\sin \left (x \right ) \end{align*}

✗ Maple

ode:=3*y(x)*diff(diff(y(x),x),x) = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=3*y[x]*D[y[x],{x,2}]==Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x)*Derivative(y(x), (x, 2)) - sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve 3*y(x)*Derivative(y(x), (x, 2)) - sin(x)