29.21.2 problem 578

Internal problem ID [5172]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 578
Date solved : Monday, January 27, 2025 at 10:17:12 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.696 (sec). Leaf size: 79

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

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