Internal problem ID [5779]
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: Example 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x +y-2}{y-x -4}=0} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 32
dsolve(diff(y(x),x)=(x+y(x)-2)/(y(x)-x-4),y(x), singsol=all)
\[ y \left (x \right ) = 3-\frac {-c_{1} \left (x +1\right )+\sqrt {2 \left (x +1\right )^{2} c_{1}^{2}+1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.807 (sec). Leaf size: 59
DSolve[y'[x]==(x+y[x]-2)/(y[x]-x-4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {-2 x^2-4 x-16-c_1}+x+4 y(x)\to i \sqrt {-2 x^2-4 x-16-c_1}+x+4 \end{align*}