85.1.7 problem 1 (i)

Internal problem ID [22412]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 1 (i)
Date solved : Thursday, October 02, 2025 at 08:38:38 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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