15.4.7 problem 7

Internal problem ID [2920]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 7
Date solved : Monday, January 27, 2025 at 06:55:53 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 16

dsolve((y(x)*cos(x)-2*sin(y(x)))=(2*x*cos(y(x))-sin(x))*diff(y(x),x),y(x), singsol=all)
 

\[ y \sin \left (x \right )-2 x \sin \left (y\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.152 (sec). Leaf size: 19

DSolve[(y[x]*Cos[x]-2*Sin[y[x]])==(2*x*Cos[y[x]]-Sin[x])*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[2 x \sin (y(x))-y(x) \sin (x)=c_1,y(x)] \]