75.7.9 problem 184

Internal problem ID [16802]
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 : 184
Date solved : Tuesday, January 28, 2025 at 09:29:49 AM
CAS classification : [_exact]

\begin{align*} \sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.064 (sec). Leaf size: 21

dsolve(( sin(y(x))+y(x)*sin(x)+1/x )+( x*cos(y(x))-cos(x)+1/y(x) )*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.371 (sec). Leaf size: 66

DSolve[( Sin[y[x]]+y[x]*Sin[x]+1/x )+( x*Cos[y[x]]-Cos[x]+1/y[x] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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