75.4.13 problem 58

Internal problem ID [16715]
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
Date solved : Tuesday, January 28, 2025 at 09:19:19 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.721 (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)
 

\[ y = -\frac {\operatorname {LambertW}\left (-\left (\sec \left (x \right )+c_{1} \right ) {\mathrm e}^{-1}\right )}{\sec \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 60.155 (sec). Leaf size: 29

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

\[ y(x)\to \frac {\cos (x) W\left (\frac {-\sec (x)+c_1}{e}\right )}{-1+c_1 \cos (x)} \]