88.12.9 problem 11

Internal problem ID [24065]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:56:48 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 22

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

\[ \frac {x^{2}}{2}+{\mathrm e}^{x} \cos \left (y\right )-\frac {y^{2}}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.21 (sec). Leaf size: 30

ode=(Exp[x]*Cos[y[x]]+x) - (Exp[x]*Sin[y[x]]+y[x])*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\frac {x^2}{2}+\frac {y(x)^2}{2}-e^x \cos (y(x))=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out