Internal problem ID [4555]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order.
page 315
Problem number: 10.3.9 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {3 x y^{\prime }+y+y^{4} x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 124
dsolve(3*x*diff(y(x),x)+y(x)+x^2*y(x)^4=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (\left (c_{1}+x \right )^{2} x^{2}\right )^{\frac {1}{3}}}{\left (c_{1}+x \right ) x} \\ y \relax (x ) = -\frac {\left (\left (c_{1}+x \right )^{2} x^{2}\right )^{\frac {1}{3}}}{2 \left (c_{1}+x \right ) x}-\frac {i \sqrt {3}\, \left (\left (c_{1}+x \right )^{2} x^{2}\right )^{\frac {1}{3}}}{2 \left (c_{1}+x \right ) x} \\ y \relax (x ) = -\frac {\left (\left (c_{1}+x \right )^{2} x^{2}\right )^{\frac {1}{3}}}{2 \left (c_{1}+x \right ) x}+\frac {i \sqrt {3}\, \left (\left (c_{1}+x \right )^{2} x^{2}\right )^{\frac {1}{3}}}{2 \left (c_{1}+x \right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.285 (sec). Leaf size: 61
DSolve[3*x*y'[x]+y[x]+x^2*y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt [3]{x (x+c_1)}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{x (x+c_1)}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{x (x+c_1)}} \\ y(x)\to 0 \\ \end{align*}