Internal problem ID [5305]
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 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x +y-x^{3} y^{6}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 265
dsolve(x*diff(y(x),x)+(y(x)-x^3*y(x)^6)=0,y(x), singsol=all)
\begin{align*} y = \frac {2^{\frac {1}{5}} \left (x^{2} \left (2 c_{1} x^{2}+5\right )^{4}\right )^{\frac {1}{5}}}{x \left (2 c_{1} x^{2}+5\right )} y = \frac {\left (-\frac {\sqrt {5}}{4}-\frac {1}{4}-\frac {i \sqrt {2}\, \sqrt {5-\sqrt {5}}}{4}\right ) 2^{\frac {1}{5}} \left (x^{2} \left (2 c_{1} x^{2}+5\right )^{4}\right )^{\frac {1}{5}}}{x \left (2 c_{1} x^{2}+5\right )} y = \frac {\left (-\frac {\sqrt {5}}{4}-\frac {1}{4}+\frac {i \sqrt {2}\, \sqrt {5-\sqrt {5}}}{4}\right ) 2^{\frac {1}{5}} \left (x^{2} \left (2 c_{1} x^{2}+5\right )^{4}\right )^{\frac {1}{5}}}{x \left (2 c_{1} x^{2}+5\right )} y = \frac {\left (\frac {\sqrt {5}}{4}-\frac {1}{4}-\frac {i \sqrt {2}\, \sqrt {5+\sqrt {5}}}{4}\right ) 2^{\frac {1}{5}} \left (x^{2} \left (2 c_{1} x^{2}+5\right )^{4}\right )^{\frac {1}{5}}}{x \left (2 c_{1} x^{2}+5\right )} y = \frac {\left (\frac {\sqrt {5}}{4}-\frac {1}{4}+\frac {i \sqrt {2}\, \sqrt {5+\sqrt {5}}}{4}\right ) 2^{\frac {1}{5}} \left (x^{2} \left (2 c_{1} x^{2}+5\right )^{4}\right )^{\frac {1}{5}}}{x \left (2 c_{1} x^{2}+5\right )} \end{align*}
✓ Solution by Mathematica
Time used: 0.472 (sec). Leaf size: 141
DSolve[x*y'[x]+(y[x]-x^3*y[x]^6)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [5]{-2}}{\sqrt [5]{x^3 \left (5+2 c_1 x^2\right )}} y(x)\to \frac {1}{\sqrt [5]{\frac {5 x^3}{2}+c_1 x^5}} y(x)\to \frac {(-1)^{2/5}}{\sqrt [5]{\frac {5 x^3}{2}+c_1 x^5}} y(x)\to -\frac {(-1)^{3/5}}{\sqrt [5]{\frac {5 x^3}{2}+c_1 x^5}} y(x)\to \frac {(-1)^{4/5}}{\sqrt [5]{\frac {5 x^3}{2}+c_1 x^5}} y(x)\to 0 \end{align*}