5.23 problem 23

Internal problem ID [7964]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 23
Date solved : Monday, October 21, 2024 at 04:39:57 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

Solve

\begin{align*} y^{\prime }&=\frac {x y+3 x -2 y+6}{x y-3 x -2 y+6} \end{align*}

Unknown ode type.

5.23.1 Maple step by step solution

\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {x y+3 x -2 y+6}{x y-3 x -2 y+6} \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {x y+3 x -2 y+6}{x y-3 x -2 y+6} \end {array} \]

5.23.2 Maple trace

Methods for first order ODEs:
 

5.23.3 Maple dsolve solution

Solving time : 0.014 (sec)
Leaf size : maple_leaf_size

dsolve(diff(y(x),x) = (x*y(x)+3*x-2*y(x)+6)/(x*y(x)-3*x-2*y(x)+6), 
       y(x),singsol=all)
 

\[ \text {No solution found} \]

5.23.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

DSolve[{D[y[x],x]==(x*y[x]+3*x-2*y[x]+6)/(x*y[x]-3*x-2*y[x]+6),{}}, 
       y[x],x,IncludeSingularSolutions->True]
 

Not solved