38.2.21 problem 21

Internal problem ID [6450]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:04:33 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+y&=x y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(diff(y(x),x)+y(x)=x*y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= -\frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 x} c_1 +4 x}} \\ y &= \frac {2}{\sqrt {2+4 \,{\mathrm e}^{2 x} c_1 +4 x}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.203 (sec). Leaf size: 50

DSolve[D[y[x],x]+y[x]==x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}} \\ y(x)\to \frac {1}{\sqrt {x+c_1 e^{2 x}+\frac {1}{2}}} \\ y(x)\to 0 \\ \end{align*}