47.2.40 problem 38

Internal problem ID [7456]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 38
Date solved : Monday, January 27, 2025 at 03:00:40 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 49

dsolve(y(x)+2=(2*x+y(x)-4)*diff(y(x),x),y(x), singsol=all)
 

\begin{align*} y &= \frac {1-4 c_{1} +\sqrt {1+4 \left (x -3\right ) c_{1}}}{2 c_{1}} \\ y &= \frac {1-4 c_{1} -\sqrt {1+4 \left (x -3\right ) c_{1}}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 82

DSolve[y[x]+2==(2*x+y[x]-4)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {1+4 c_1 (x-3)}-1+4 c_1}{2 c_1} \\ y(x)\to \frac {\sqrt {1+4 c_1 (x-3)}+1-4 c_1}{2 c_1} \\ y(x)\to -2 \\ y(x)\to \text {Indeterminate} \\ y(x)\to 1-x \\ \end{align*}