Internal problem ID [3102]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 10, page 47
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {\left (x +3 y^{4} x^{3}\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 129
dsolve((x+3*x^3*y(x)^4)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\sqrt {-6 x c_{1} \left (-x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} y \left (x \right ) = \frac {\sqrt {-6 x c_{1} \left (-x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} y \left (x \right ) = -\frac {\sqrt {6}\, \sqrt {x c_{1} \left (x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} y \left (x \right ) = \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: 10.044 (sec). Leaf size: 166
DSolve[(x+3*x^3*y[x]^4)*y'[x]+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*}