38.2.23 problem 23

Internal problem ID [6452]
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 : 23
Date solved : Monday, January 27, 2025 at 02:04:34 PM
CAS classification : [_Bernoulli]

\begin{align*} 2 y^{\prime }+y&=y^{3} \left (x -1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(2*diff(y(x),x)+y(x)=y(x)^3*(x-1),y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{x} c_1 +x}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{x} c_1 +x}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.861 (sec). Leaf size: 40

DSolve[2*D[y[x],x]+y[x]==y[x]^3*(x-1),y[x],x,IncludeSingularSolutions -> True]
 

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