Internal problem ID [4617]
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: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x y y^{\prime }+y^{2}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 45
dsolve(2*x*y(x)*diff(y(x),x)=x^2-y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {3}\, \sqrt {x \left (x^{3}+3 c_{1}\right )}}{3 x} \\ y \relax (x ) = \frac {\sqrt {3}\, \sqrt {x \left (x^{3}+3 c_{1}\right )}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 56
DSolve[2*x*y[x]*y'[x]==x^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ y(x)\to \frac {\sqrt {x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ \end{align*}