Internal problem ID [10141]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 15. Page
22
Problem number: Ex 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {2 x^{3} y-y^{2}-\left (2 x^{4}+y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 47
dsolve((2*x^3*y(x)-y(x)^2)-(2*x^4+x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1} \left (\sqrt {4 x^{4}+c_{1}^{2}}+c_{1}\right )}{2 x} \\ y \relax (x ) = \frac {c_{1} \left (c_{1}-\sqrt {4 x^{4}+c_{1}^{2}}\right )}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.849 (sec). Leaf size: 76
DSolve[(2*x^3*y[x]-y[x]^2)-(2*x^4+x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^4}{-x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to -\frac {2 x^4}{x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}