29.26.3 problem 736

Internal problem ID [5324]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 736
Date solved : Monday, January 27, 2025 at 11:12:40 AM
CAS classification : unknown

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

✓ Solution by Maple

Time used: 0.171 (sec). Leaf size: 33

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

\[ \frac {\left (-2 \sin \left (A \right ) \sin \left (x \right )+\cos \left (y \left (x \right )\right )\right ) \sin \left (y \left (x \right )\right )}{2}+\frac {\cos \left (x \right ) \sin \left (x \right )}{2}+\frac {y \left (x \right )}{2}+c_{1} +\frac {x}{2} = 0 \]

✓ Solution by Mathematica

Time used: 0.416 (sec). Leaf size: 43

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

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