Internal problem ID [3222]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 476.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {3 y y^{\prime }+5 \cot \relax (x ) \cot \relax (y) \left (\cos ^{2}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.765 (sec). Leaf size: 60
dsolve(3*y(x)*diff(y(x),x)+5*cot(x)*cot(y(x))*cos(y(x))^2 = 0,y(x), singsol=all)
\[ \frac {-3 \tan \left (y \relax (x )\right ) \cos \left (2 y \relax (x )\right )+10 \ln \left (\sin \relax (x )\right ) \cos \left (2 y \relax (x )\right )+10 c_{1} \cos \left (2 y \relax (x )\right )-3 \tan \left (y \relax (x )\right )+10 \ln \left (\sin \relax (x )\right )+10 c_{1}+6 y \relax (x )}{10 \cos \left (2 y \relax (x )\right )+10} = 0 \]
✓ Solution by Mathematica
Time used: 0.516 (sec). Leaf size: 30
DSolve[3 y[x] y'[x]+5 Cot[x] Cot[y[x]] Cos[y[x]]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [40 \sin (x) e^{\frac {3}{10} \left (y(x) \sec ^2(y(x))-\tan (y(x))\right )}=c_1,y(x)\right ] \]