Internal problem ID [112]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {3 x^{2}+2 x y^{2}+\left (2 y x^{2}+4 y^{3}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 117
dsolve(3*x^2+2*x*y(x)^2+(2*x^2*y(x)+4*y(x)^3)*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x^{2}-2 \sqrt {x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2 x^{2}-2 \sqrt {x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y \relax (x ) = -\frac {\sqrt {-2 x^{2}+2 \sqrt {x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y \relax (x ) = \frac {\sqrt {-2 x^{2}+2 \sqrt {x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.328 (sec). Leaf size: 151
DSolve[3*x^2+2*x*y[x]^2+(2*x^2*y[x]+4*y[x]^3)*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2-\sqrt {(x-4) x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2-\sqrt {(x-4) x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-x^2+\sqrt {(x-4) x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2+\sqrt {(x-4) x^3+4 c_1}}}{\sqrt {2}} \\ \end{align*}