Internal problem ID [5081]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {\left (x^{3}+x y^{2}\right ) y^{\prime }-2 y^{3}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve((x^3+x*y(x)^2)*diff(y(x),x)=2*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (\frac {c_{1} x}{2}-\frac {\sqrt {c_{1}^{2} x^{2}+4}}{2}\right ) x y \left (x \right ) = \left (\frac {c_{1} x}{2}+\frac {\sqrt {c_{1}^{2} x^{2}+4}}{2}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 1.2 (sec). Leaf size: 83
DSolve[(x^3+x*y[x]^2)*y'[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*}