Internal problem ID [14985]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 58.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.36 (sec). Leaf size: 21
dsolve(y(x)^2*sin(x)+cos(x)^2*ln(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-\left (\sec \left (x \right )+c_{1} \right ) {\mathrm e}^{-1}\right )}{\sec \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 60.174 (sec). Leaf size: 29
DSolve[y[x]^2*Sin[x]+Cos[x]^2*Log[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (x) W\left (\frac {-\sec (x)+c_1}{e}\right )}{-1+c_1 \cos (x)} \]