Internal problem ID [3858]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 608.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {\left (x^{4}+y^{2}\right ) y^{\prime }-4 y x^{3}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 67
dsolve((x^4+y(x)^2)*diff(y(x),x) = 4*x^3*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (\frac {2 x^{2}+c_{1} -\sqrt {4 x^{4}+c_{1}^{2}}}{2 x^{2}}-1\right ) x^{2} y \left (x \right ) = \left (\frac {2 x^{2}+c_{1} +\sqrt {4 x^{4}+c_{1}^{2}}}{2 x^{2}}-1\right ) x^{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 58
DSolve[(x^4+y[x]^2)y'[x]==4 x^3 y[x],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*}