60.1.347 problem 348

Internal problem ID [10361]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 348
Date solved : Monday, January 27, 2025 at 07:30:38 PM
CAS classification : [_exact]

\begin{align*} \left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }+y \cos \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))+sin(x))*diff(y(x),x)+y(x)*cos(x)+sin(y(x)) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 56

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

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