57.1.58 problem 58

Internal problem ID [9042]
Book : First order enumerated odes
Section : section 1
Problem number : 58
Date solved : Monday, January 27, 2025 at 05:27:54 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} {y^{\prime }}^{4}&=\frac {1}{x y^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.080 (sec). Leaf size: 121

dsolve(diff(y(x),x)^4=1/(x*y(x)^3),y(x), singsol=all)
 

\begin{align*} -\frac {7 x^{3}-3 \left (x^{3} y\right )^{{3}/{4}} y+c_{1} x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \frac {-7 x^{3}+3 i \left (x^{3} y\right )^{{3}/{4}} y-c_{1} x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \frac {7 x^{3}+3 i \left (x^{3} y\right )^{{3}/{4}} y-c_{1} x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \frac {7 x^{3}+3 \left (x^{3} y\right )^{{3}/{4}} y-c_{1} x^{{9}/{4}}}{x^{{9}/{4}}} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.709 (sec). Leaf size: 129

DSolve[(D[y[x],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*}