20.5.12 problem Problem 12

Internal problem ID [3695]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number : Problem 12
Date solved : Monday, January 27, 2025 at 07:55:29 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 15

dsolve((sin(y(x))+y(x)*cos(x))+(x*cos(y(x))+sin(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) \sin \left (x \right )+x \sin \left (y \left (x \right )\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 17

DSolve[(Sin[y[x]]+y[x]*Cos[x])+(x*Cos[y[x]]+Sin[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[x \sin (y(x))+y(x) \sin (x)=c_1,y(x)] \]