66.1.43 problem Problem 57

Internal problem ID [13890]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 57
Date solved : Tuesday, January 28, 2025 at 06:07:34 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y-3}{-x +y+1} \end{align*}

✓ Solution by Maple

Time used: 1.540 (sec). Leaf size: 30

dsolve(diff(y(x),x)= (x+y(x)-3)/(1-x+y(x)),y(x), singsol=all)
 

\[ y = \frac {-\sqrt {2 \left (x -2\right )^{2} c_{1}^{2}+1}+c_{1} \left (x -1\right )}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 59

DSolve[D[y[x],x]== (x+y[x]-3)/(1-x+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {-2 x^2+8 x-1-c_1}+x-1 \\ y(x)\to i \sqrt {-2 x^2+8 x-1-c_1}+x-1 \\ \end{align*}