Internal problem ID [3350]
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]
Solve \begin {gather*} \boxed {\left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (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 \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}+c_{1}+\sqrt {4 x^{4}+c_{1}^{2}}}{2 x^{2}}-1\right ) x^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.268 (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*}