Internal problem ID [2558]
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]
\[ \boxed {y^{\prime }-y^{3} \sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x)=y(x)^3*sin(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{\sqrt {c_{1} +2 \cos \left (x \right )}} y \left (x \right ) = -\frac {1}{\sqrt {c_{1} +2 \cos \left (x \right )}} \end{align*}
✓ Solution by Mathematica
Time used: 0.207 (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*}