84.5.2 problem 3.1 (b)

Internal problem ID [22089]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.1 (b)
Date solved : Thursday, October 02, 2025 at 08:23:48 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : The given ODE -x*sin(y(x)) - exp(x) + Derivative(y(x), x) cannot be solved by the lie group method