Internal problem ID [7374]
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]
\[ \boxed {{y^{\prime }}^{4}-\frac {1}{y^{3} x}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 123
dsolve(diff(y(x),x)^4=1/(x*y(x)^3),y(x), singsol=all)
\begin{align*} -\frac {7 x^{3}-3 y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}+c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \frac {-7 x^{3}+3 i y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}-c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \frac {7 x^{3}+3 i y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}-c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \frac {7 x^{3}+3 y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}-c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.225 (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*}