60.1.354 problem 355

Internal problem ID [10368]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 355
Date solved : Monday, January 27, 2025 at 07:33:14 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 59

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

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