Internal problem ID [6622]
Book: First order enumerated odes
Section: section 1
Problem number: 59.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {1}{x^{3} y^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.21 (sec). Leaf size: 185
dsolve(diff(y(x),x)^2=1/(x^3*y(x)^4),y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = \left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 157
DSolve[(y'[x])^2==1/(x^3*y[x]^4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt [3]{-3} \sqrt [3]{-\frac {2}{\sqrt {x}}+c_1} \\ y(x)\to \sqrt [3]{3} \sqrt [3]{-\frac {2}{\sqrt {x}}+c_1} \\ y(x)\to \sqrt [3]{-\frac {2}{\sqrt {x}}+c_1} \text {Root}\left [\text {$\#$1}^3-3\&,3\right ] \\ y(x)\to -\sqrt [3]{-3} \sqrt [3]{\frac {2}{\sqrt {x}}+c_1} \\ y(x)\to \sqrt [3]{3} \sqrt [3]{\frac {2}{\sqrt {x}}+c_1} \\ y(x)\to \sqrt [3]{\frac {2}{\sqrt {x}}+c_1} \text {Root}\left [\text {$\#$1}^3-3\&,3\right ] \\ \end{align*}