32.6.30 problem Exercise 12.30, page 103

Internal problem ID [5895]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.30, page 103
Date solved : Monday, January 27, 2025 at 01:25:08 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (6 y x +x^{2}+3\right ) y^{\prime }+3 y^{2}+2 y x +2 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 75

dsolve((6*x*y(x)+x^2+3)*diff(y(x),x)+3*y(x)^2+2*x*y(x)+2*x=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {-x^{2}-3+\sqrt {x^{4}-12 x^{3}-12 c_{1} x +6 x^{2}+9}}{6 x} \\ y \left (x \right ) &= \frac {-x^{2}-3-\sqrt {x^{4}-12 x^{3}-12 c_{1} x +6 x^{2}+9}}{6 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.644 (sec). Leaf size: 83

DSolve[(6*x*y[x]+x^2+3)*D[y[x],x]+3*y[x]^2+2*x*y[x]+2*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^2+\sqrt {x^4-12 x^3+6 x^2+36 c_1 x+9}+3}{6 x} \\ y(x)\to -\frac {x^2-\sqrt {x^4-12 x^3+6 x^2+36 c_1 x+9}+3}{6 x} \\ \end{align*}