Internal problem ID [7939]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 359.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {3 y^{\prime } \sin \relax (x ) \sin \relax (y)+5 \left (\cos ^{4}\relax (x )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(3*diff(y(x),x)*sin(x)*sin(y(x))+5*cos(x)^4*y(x) = 0,y(x), singsol=all)
\[ \frac {3 \sinIntegral \left (y \relax (x )\right )}{5}+c_{1}+\ln \left (\csc \relax (x )-\cot \relax (x )\right )+\frac {\cos \left (3 x \right )}{12}+\frac {5 \cos \relax (x )}{4} = 0 \]
✓ Solution by Mathematica
Time used: 0.915 (sec). Leaf size: 47
DSolve[5*Cos[x]^4*y[x] + 3*Sin[x]*Sin[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {SinIntegral}^{(-1)}\left (-\frac {5}{36} \left (15 \cos (x)+\cos (3 x)+12 \left (\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )\right )\right )+c_1\right ) \\ y(x)\to 0 \\ \end{align*}