29.20.11 problem 556

Internal problem ID [5152]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 556
Date solved : Monday, January 27, 2025 at 10:16:06 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 75

dsolve((3+6*x*y(x)+x^2)*diff(y(x),x)+2*x+2*x*y(x)+3*y(x)^2 = 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: 0.615 (sec). Leaf size: 83

DSolve[(3+6 x y[x]+x^2)D[y[x],x]+2 x+2 x y[x]+3 y[x]^2==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*}