60.1.351 problem 352

Internal problem ID [10365]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 352
Date solved : Monday, January 27, 2025 at 07:32:24 PM
CAS classification : unknown

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

✓ Solution by Maple

Time used: 0.217 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.530 (sec). Leaf size: 162

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

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