Internal problem ID [5474]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page
32
Problem number: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x y^{\prime }+y+3 x^{3} y^{4} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.071 (sec). Leaf size: 129
dsolve(x*diff(y(x),x)+y(x)+3*x^3*y(x)^4*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-6 x c_{1} \left (-x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y \relax (x ) = \frac {\sqrt {-6 x c_{1} \left (-x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y \relax (x ) = -\frac {\sqrt {6}\, \sqrt {x c_{1} \left (x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y \relax (x ) = \frac {\sqrt {6}\, \sqrt {x c_{1} \left (x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.873 (sec). Leaf size: 166
DSolve[x*y'[x]+y[x]+3*x^3*y[x]^4*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {c_1-\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {c_1-\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}}}{\sqrt {3}} \\ y(x)\to -\frac {\sqrt {\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}+c_1}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}+c_1}}{\sqrt {3}} \\ y(x)\to 0 \\ \end{align*}