Internal problem ID [5063]
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]
\[ \boxed {3 x y^{\prime }+y+y^{4} x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 88
dsolve(3*x*diff(y(x),x)+y(x)+x^2*y(x)^4=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (\left (x +c_{1} \right )^{2} x^{2}\right )^{\frac {1}{3}}}{\left (x +c_{1} \right ) x} \\ y \left (x \right ) &= -\frac {\left (\left (x +c_{1} \right )^{2} x^{2}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2 \left (x +c_{1} \right ) x} \\ y \left (x \right ) &= \frac {\left (\left (x +c_{1} \right )^{2} x^{2}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2 \left (x +c_{1} \right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.3 (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*}