Internal problem ID [5314]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {2 x y^{5}-y+2 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 131
dsolve((2*x*y(x)^5-y(x))+2*x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \frac {\sqrt {-3 \sqrt {12 x^{3}+9 c_{1}}\, x}}{\sqrt {12 x^{3}+9 c_{1}}} y = \frac {\sqrt {3}\, \sqrt {\sqrt {12 x^{3}+9 c_{1}}\, x}}{\sqrt {12 x^{3}+9 c_{1}}} y = -\frac {\sqrt {-3 \sqrt {12 x^{3}+9 c_{1}}\, x}}{\sqrt {12 x^{3}+9 c_{1}}} y = -\frac {\sqrt {3}\, \sqrt {\sqrt {12 x^{3}+9 c_{1}}\, x}}{\sqrt {12 x^{3}+9 c_{1}}} \end{align*}
✓ Solution by Mathematica
Time used: 0.214 (sec). Leaf size: 109
DSolve[(2*x*y[x]^5-y[x])+2*x*y'[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*}