Internal problem ID [3413]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 674.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (1-x^{4} y^{2}\right ) y^{\prime }-y^{3} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.161 (sec). Leaf size: 191
dsolve((1-x^4*y(x)^2)*diff(y(x),x) = x^3*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-c_{1}-\sqrt {c_{1} x^{4}+c_{1}^{2}}}\, \left (\frac {-c_{1}-\sqrt {c_{1} x^{4}+c_{1}^{2}}}{c_{1}}+2\right )}{x^{4}} \\ y \relax (x ) = \frac {\sqrt {-c_{1}+\sqrt {c_{1} x^{4}+c_{1}^{2}}}\, \left (\frac {-c_{1}+\sqrt {c_{1} x^{4}+c_{1}^{2}}}{c_{1}}+2\right )}{x^{4}} \\ y \relax (x ) = -\frac {\sqrt {-c_{1}-\sqrt {c_{1} x^{4}+c_{1}^{2}}}\, \left (\frac {-c_{1}-\sqrt {c_{1} x^{4}+c_{1}^{2}}}{c_{1}}+2\right )}{x^{4}} \\ y \relax (x ) = -\frac {\sqrt {-c_{1}+\sqrt {c_{1} x^{4}+c_{1}^{2}}}\, \left (\frac {-c_{1}+\sqrt {c_{1} x^{4}+c_{1}^{2}}}{c_{1}}+2\right )}{x^{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.63 (sec). Leaf size: 122
DSolve[(1-x^4 y[x]^2)y'[x]==x^3 y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\frac {1-\sqrt {1+4 c_1 x^4}}{x^4}} \\ y(x)\to \sqrt {\frac {1-\sqrt {1+4 c_1 x^4}}{x^4}} \\ y(x)\to -\sqrt {\frac {1+\sqrt {1+4 c_1 x^4}}{x^4}} \\ y(x)\to \sqrt {\frac {1+\sqrt {1+4 c_1 x^4}}{x^4}} \\ y(x)\to 0 \\ \end{align*}