87.16.16 problem 16

Internal problem ID [23585]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:43:13 PM
CAS classification : [NONE]

\begin{align*} 3 x y^{\prime \prime \prime }-4 y x&=\cos \left (y\right ) \end{align*}

✗ Maple

ode:=3*x*diff(diff(diff(y(x),x),x),x)-4*x*y(x) = cos(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=3*x*D[y[x],{x,3}]-4*x*y[x]==Cos[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*y(x) + 3*x*Derivative(y(x), (x, 3)) - cos(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -4*x*y(x) + 3*x*Derivative(y(x), (x, 3)) - cos(y(x))