60.1.360 problem 361

Internal problem ID [10374]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 361
Date solved : Monday, January 27, 2025 at 07:36:46 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.394 (sec). Leaf size: 94

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

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