Internal problem ID [14432]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (-x +2 y\right ) y^{\prime }=-2 x +2} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.531 (sec). Leaf size: 22
dsolve([(2*x-y(x)-2)+(2*y(x)-x)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{2}+\frac {\sqrt {-3 x^{2}+8 x +4}}{2} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 29
DSolve[{(2*x-y[x]-2)+(2*y[x]-x)*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x-i \sqrt {3 x^2-8 x-4}\right ) \]