Internal problem ID [7375]
Book: First order enumerated odes
Section: section 1
Problem number: 59.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {{y^{\prime }}^{2}-\frac {1}{x^{3} y^{4}}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 137
dsolve(diff(y(x),x)^2=1/(x^3*y(x)^4),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ y \left (x \right ) &= \left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.775 (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 (-1)^{2/3} \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]{3} \sqrt [3]{\frac {2}{\sqrt {x}}+c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{3} \sqrt [3]{\frac {2}{\sqrt {x}}+c_1} \\ \end{align*}