Internal problem ID [10118]
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 10.
Homogeneous equations. Page 15
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {2 x^{2} y+3 y^{3}-\left (x^{3}+2 y^{2} x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 89
dsolve((2*x^2*y(x)+3*y(x)^3)-(x^3+2*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2-2 \sqrt {4 x^{2} c_{1}+1}}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {-2-2 \sqrt {4 x^{2} c_{1}+1}}\, x}{2} \\ y \relax (x ) = -\frac {\sqrt {-2+2 \sqrt {4 x^{2} c_{1}+1}}\, x}{2} \\ y \relax (x ) = \frac {\sqrt {-2+2 \sqrt {4 x^{2} c_{1}+1}}\, x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 41.277 (sec). Leaf size: 277
DSolve[(2*x^2*y[x]+3*y[x]^3)-(x^3+2*x*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2-\sqrt {x^4+4 e^{2 c_1} x^6}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-x^2-\sqrt {x^4+4 e^{2 c_1} x^6}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-x^2+\sqrt {x^4+4 e^{2 c_1} x^6}}}{\sqrt {2}} \\ y(x)\to \sqrt {-\frac {x^2}{2}+\frac {1}{2} \sqrt {x^4+4 e^{2 c_1} x^6}} \\ y(x)\to -\frac {\sqrt {-\sqrt {x^4}-x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sqrt {x^4}-x^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {x^4}-x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {x^4}-x^2}}{\sqrt {2}} \\ \end{align*}