20.2.15 problem Problem 15

Internal problem ID [3607]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 15
Date solved : Monday, January 27, 2025 at 07:47:29 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 5

dsolve([diff(y(x),x)=y(x)^3*sin(x),y(0) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 6

DSolve[{D[y[x],x]==y[x]^3*Sin[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 0 \]