Internal problem ID [15073]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\frac {y+\sin \left (x \right ) \cos \left (y x \right )^{2}}{\cos \left (y x \right )^{2}}+\left (\frac {x}{\cos \left (y x \right )^{2}}+\sin \left (y\right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ \tan \left (x y \left (x \right )\right )-\cos \left (x \right )-\cos \left (y \left (x \right )\right )+c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (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]] )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved