19.1.15 problem 15

Internal problem ID [3529]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:40:44 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.170 (sec). Leaf size: 49

DSolve[D[y[x],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*}