Internal problem ID [2057]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.6, page 50
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-y \tan \relax (x )-8 \left (\sin ^{3}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
dsolve(diff(y(x),x)-y(x)*tan(x)=8*sin(x)^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {-\cos \left (2 x \right )+\frac {\cos \left (4 x \right )}{4}+c_{1}}{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 19
DSolve[y'[x]-y[x]*Tan[x]==8*Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \sin ^3(x) \tan (x)+c_1 \sec (x) \\ \end{align*}