62.5.2 problem Ex 2

Internal problem ID [12817]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 12. Page 18
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:24:34 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.702 (sec). Leaf size: 69

DSolve[(2*y[x]+3*x*y[x]^2)+(x+2*x^2*y[x])*D[y[x],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*}