67.2.17 problem Problem 2(b)

Internal problem ID [13903]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 2(b)
Date solved : Monday, March 31, 2025 at 08:17:34 AM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2}&=\sin \left (x \right ) \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,3}]+x*D[y[x],{x,2}]-y[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(x*Derivative(y(x), (x, 2)) - y(x)**2 - sin(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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