29.19.20 problem 533

Internal problem ID [5129]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 533
Date solved : Monday, January 27, 2025 at 10:13:25 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 y x -y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.097 (sec). Leaf size: 69

dsolve(x*(4*x-y(x))*diff(y(x),x)+4*x^2-6*x*y(x)-y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.638 (sec). Leaf size: 90

DSolve[x(4 x -y[x])D[y[x],x]+4 x^2-6 x y[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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