Internal problem ID [7778]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 198.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\cos \relax (x ) \sin \relax (x ) y^{\prime }-y-\left (\sin ^{3}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(sin(x)*cos(x)*diff(y(x),x) - y(x) - sin(x)^3=0,y(x), singsol=all)
\[ y \relax (x ) = \left (-\cos \relax (x )+c_{1}\right ) \tan \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 15
DSolve[Sin[x]*Cos[x]*y'[x] - y[x] - Sin[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sin (x)+c_1 \tan (x) \\ \end{align*}