75.7.10 problem 185

Internal problem ID [16803]
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 : 185
Date solved : Tuesday, January 28, 2025 at 09:30:25 AM
CAS classification : [_exact]

\begin{align*} \frac {y+\sin \left (x \right ) \cos \left (y x \right )^{2}}{\cos \left (y x \right )^{2}}+\left (\frac {x}{\cos \left (y x \right )^{2}}+\sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.290 (sec). Leaf size: 19

dsolve(( (y(x)+sin(x)*cos(x*y(x))^2 )/cos(x*y(x))^2 )+( x/cos(x*y(x))^2+sin(y(x)) )*diff(y(x),x)=0,y(x), singsol=all)
 

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[( (y[x]+Sin[x]*Cos[x*y[x]]^2 )/Cos[x*y[x]]^2 )+( x/Cos[x*y[x]]^2+Sin[y[x]] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved