29.20.1 problem 546

Internal problem ID [5142]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 546
Date solved : Monday, January 27, 2025 at 10:14:13 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 63

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

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

✓ Solution by Mathematica

Time used: 0.583 (sec). Leaf size: 75

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

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