Internal problem ID [7889]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 310.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\[ \boxed {\left (2 y^{3}+5 y x^{2}\right ) y^{\prime }+5 y^{2} x +x^{3}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 125
dsolve((2*y(x)^3+5*x^2*y(x))*diff(y(x),x)+5*x*y(x)^2+x^3 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\sqrt {-10 x^{2} c_{1} -2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y \left (x \right ) = \frac {\sqrt {-10 x^{2} c_{1} -2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y \left (x \right ) = -\frac {\sqrt {-10 x^{2} c_{1} +2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y \left (x \right ) = \frac {\sqrt {-10 x^{2} c_{1} +2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 23.504 (sec). Leaf size: 295
DSolve[x^3 + 5*x*y[x]^2 + (5*x^2*y[x] + 2*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ \end{align*}