Internal problem ID [2049]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y^{3} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 25
dsolve(diff(y(x),x)=y(x)^3*sin(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {c_{1}+2 \cos \relax (x )}} \\ y \relax (x ) = -\frac {1}{\sqrt {c_{1}+2 \cos \relax (x )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 49
DSolve[y'[x]==y[x]^3*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {\cos (x)-c_1}} \\ y(x)\to \frac {1}{\sqrt {2} \sqrt {\cos (x)-c_1}} \\ y(x)\to 0 \\ \end{align*}