37.2.9 problem 10.3.9 (b)

Internal problem ID [6406]
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)
Date solved : Monday, January 27, 2025 at 02:00:46 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 x y^{\prime }+y+x^{2} y^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 86

dsolve(3*x*diff(y(x),x)+y(x)+x^2*y(x)^4=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (\left (x +c_1 \right )^{2} x^{2}\right )^{{1}/{3}}}{\left (x +c_1 \right ) x} \\ y &= -\frac {\left (\left (x +c_1 \right )^{2} x^{2}\right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2 \left (x +c_1 \right ) x} \\ y &= \frac {\left (\left (x +c_1 \right )^{2} x^{2}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2 \left (x +c_1 \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.373 (sec). Leaf size: 61

DSolve[3*x*D[y[x],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*}