Internal problem ID [5295]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 26 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 y+3 x y^{2}+\left (x +2 y x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
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 {4 c_{1} x +x^{2}}}{2 x^{2}} y = -\frac {x +\sqrt {4 c_{1} x +x^{2}}}{2 x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.526 (sec). Leaf size: 69
DSolve[(2*y[x]+3*x*y[x]^2)+(x+2*x^2*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*}