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]
\[ \boxed {2 y^{5} x -y+2 x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) &= \frac {3^{\frac {1}{4}} \sqrt {-\sqrt {4 x^{3}+3 c_{1}}\, x}}{\sqrt {4 x^{3}+3 c_{1}}} \\ y \left (x \right ) &= \frac {3^{\frac {1}{4}} \sqrt {\sqrt {4 x^{3}+3 c_{1}}\, x}}{\sqrt {4 x^{3}+3 c_{1}}} \\ y \left (x \right ) &= -\frac {3^{\frac {1}{4}} \sqrt {-\sqrt {4 x^{3}+3 c_{1}}\, x}}{\sqrt {4 x^{3}+3 c_{1}}} \\ y \left (x \right ) &= -\frac {3^{\frac {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: 0.214 (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*}