40.4.17 problem 19 (s)

Internal problem ID [6657]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (s)
Date solved : Monday, January 27, 2025 at 02:17:38 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y^{5}-y+2 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 137

dsolve((2*x*y(x)^5-y(x))+2*x*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {3^{{1}/{4}} \sqrt {-\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ y &= \frac {3^{{1}/{4}} \sqrt {\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ y &= -\frac {3^{{1}/{4}} \sqrt {-\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ y &= -\frac {3^{{1}/{4}} \sqrt {\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.222 (sec). Leaf size: 109

DSolve[(2*x*y[x]^5-y[x])+2*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}} \\ y(x)\to -\frac {i \sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}} \\ y(x)\to \frac {i \sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}} \\ y(x)\to 0 \\ \end{align*}