74.8.30 problem 30

Internal problem ID [16166]
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
Date solved : Tuesday, January 28, 2025 at 08:53:21 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.997 (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)
 

\[ y = \frac {x}{2}+\frac {\sqrt {-3 x^{2}+8 x +4}}{2} \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 29

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

\[ y(x)\to \frac {1}{2} \left (x-i \sqrt {3 x^2-8 x-4}\right ) \]