Internal problem ID [7857]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 277.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (y^{2}+x^{4}\right ) y^{\prime }-4 y x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 67
dsolve((y(x)^2+x^4)*diff(y(x),x)-4*x^3*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (\frac {2 x^{2}+c_{1}+\sqrt {4 x^{4}+c_{1}^{2}}}{2 x^{2}}-1\right ) x^{2} \\ y \relax (x ) = \left (-\frac {-2 x^{2}+\sqrt {4 x^{4}+c_{1}^{2}}-c_{1}}{2 x^{2}}-1\right ) x^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.423 (sec). Leaf size: 58
DSolve[(y[x]^2+x^4)*y'[x]-4*x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {4 x^4+c_1{}^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4 x^4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}