75.7.19 problem 194

Internal problem ID [16812]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 194
Date solved : Tuesday, January 28, 2025 at 09:33:30 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 24

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

\[ y = -\arcsin \left (x +\frac {\sin \left (x \right )}{2}-\frac {\cos \left (x \right )}{2}-1+c_{1} {\mathrm e}^{-x}\right ) \]

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 67

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

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