38.1.7 problem 7

Internal problem ID [6424]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:01:19 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 44

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

\begin{align*} y &= -\frac {\left (-c_1 x +\sqrt {x^{2} c_1^{2}+4}\right ) x}{2} \\ y &= \frac {\left (c_1 x +\sqrt {x^{2} c_1^{2}+4}\right ) x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.366 (sec). Leaf size: 83

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

\begin{align*} y(x)\to -\frac {1}{2} x \left (\sqrt {4+e^{2 c_1} x^2}+e^{c_1} x\right ) \\ y(x)\to \frac {1}{2} x \left (\sqrt {4+e^{2 c_1} x^2}-e^{c_1} x\right ) \\ y(x)\to 0 \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}