29.20.22 problem 569

Internal problem ID [5163]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 569
Date solved : Monday, January 27, 2025 at 10:16:40 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (1+y x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 59

dsolve(x*(2-x*y(x))*diff(y(x),x)+2*y(x)-x*y(x)^2*(1+x*y(x)) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.161 (sec). Leaf size: 86

DSolve[x(2-x y[x])D[y[x],x]+2 y[x]-x y[x]^2(1+x y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2}{x+\sqrt {-\frac {1}{x^3}} x^2 \sqrt {-x (-4 \log (x)+1+4 c_1)}} \\ y(x)\to \frac {2}{x+\left (-\frac {1}{x^3}\right )^{3/2} x^5 \sqrt {-x (-4 \log (x)+1+4 c_1)}} \\ y(x)\to 0 \\ \end{align*}