29.21.1 problem 577

Internal problem ID [5171]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 577
Date solved : Monday, January 27, 2025 at 10:17:01 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (1+2 y x \right ) y^{\prime }+\left (2+3 y x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 45

dsolve(x*(1+2*x*y(x))*diff(y(x),x)+(2+3*x*y(x))*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.646 (sec). Leaf size: 69

DSolve[x(1+2 x y[x])D[y[x],x]+(2+3 x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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