Internal problem ID [13794]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-3 y+\left (2 y-3 x \right ) y^{\prime }=-2 x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve((2*x-3*y(x))+(2*y(x)-3*x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\frac {3 c_{1} x}{2}-\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} y \left (x \right ) = \frac {\frac {3 c_{1} x}{2}+\frac {\sqrt {5 c_{1}^{2} x^{2}+4}}{2}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.48 (sec). Leaf size: 110
DSolve[(2*x-3*y[x])+(2*y[x]-3*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (3 x-\sqrt {5 x^2+4 e^{c_1}}\right ) y(x)\to \frac {1}{2} \left (3 x+\sqrt {5 x^2+4 e^{c_1}}\right ) y(x)\to \frac {1}{2} \left (3 x-\sqrt {5} \sqrt {x^2}\right ) y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+3 x\right ) \end{align*}