35.4.6 problem 6

Internal problem ID [6124]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 6
Date solved : Monday, January 27, 2025 at 01:36:48 PM
CAS classification : unknown

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

✓ Solution by Maple

Time used: 0.312 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.390 (sec). Leaf size: 43

DSolve[(Cos[x]*Cos[y[x]]+Sin[x]^2)-(Sin[x]*Sin[y[x]]+Cos[y[x]]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \left (\frac {y(x)}{2}+\frac {1}{4} \sin (2 y(x))\right )-2 \sin (x) \cos (y(x))-x+\frac {1}{2} \sin (2 x)=c_1,y(x)\right ] \]