Internal problem ID [6621]
Book: First order enumerated odes
Section: section 1
Problem number: 58.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{4}-\frac {1}{y^{3} x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.312 (sec). Leaf size: 99
dsolve(diff(y(x),x)^4=1/(x*y(x)^3),y(x), singsol=all)
\begin{align*} \frac {3 \left (y \relax (x ) x^{3}\right )^{\frac {7}{4}}}{x^{\frac {21}{4}}}-7 x^{\frac {3}{4}}-c_{1} = 0 \\ \frac {3 i \left (y \relax (x ) x^{3}\right )^{\frac {7}{4}}}{x^{\frac {21}{4}}}-7 x^{\frac {3}{4}}-c_{1} = 0 \\ \frac {3 i \left (y \relax (x ) x^{3}\right )^{\frac {7}{4}}}{x^{\frac {21}{4}}}+7 x^{\frac {3}{4}}-c_{1} = 0 \\ \frac {3 \left (y \relax (x ) x^{3}\right )^{\frac {7}{4}}}{x^{\frac {21}{4}}}+7 x^{\frac {3}{4}}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.024 (sec). Leaf size: 129
DSolve[(y'[x])^4==1/(x*y[x]^3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (-\frac {28 x^{3/4}}{3}+7 c_1\right ){}^{4/7}}{2 \sqrt [7]{2}} \\ y(x)\to \frac {\left (7 c_1-\frac {28}{3} i x^{3/4}\right ){}^{4/7}}{2 \sqrt [7]{2}} \\ y(x)\to \frac {\left (\frac {28}{3} i x^{3/4}+7 c_1\right ){}^{4/7}}{2 \sqrt [7]{2}} \\ y(x)\to \frac {\left (\frac {28 x^{3/4}}{3}+7 c_1\right ){}^{4/7}}{2 \sqrt [7]{2}} \\ \end{align*}