87.5.11 problem 11

Internal problem ID [23304]
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 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:29:23 PM
CAS classification : [NONE]

\begin{align*} {\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=exp(x)*cos(y(x))-x^2+(exp(y(x))*sin(x)+y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(Exp[x]*Cos[y[x]]-x^2)+(Exp[y[x]]*Sin[x]+y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out