76.4.7 problem 7

Internal problem ID [17330]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 7
Date solved : Monday, March 31, 2025 at 03:53:34 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.31 (sec). Leaf size: 73

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

\[ \text {Solve}\left [\int _1^x\left (e^{K[1]} \sin (y(x))-2 \sin (K[1]) y(x)\right )dK[1]+\int _1^{y(x)}\left (2 \cos (x)+e^x \cos (K[2])-\int _1^x\left (e^{K[1]} \cos (K[2])-2 \sin (K[1])\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out