12.6.22 problem 22

Internal problem ID [1701]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 22
Date solved : Monday, January 27, 2025 at 05:30:55 AM
CAS classification : [_separable]

\begin{align*} \left (2 x -1\right ) \left (y-1\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve([((2*x-1)*(y(x)-1))+((x+2)*(x-3))*diff(y(x),x)=0,y(1) = -1],y(x), singsol=all)
 

\[ y = \frac {x^{2}-x +6}{\left (x +2\right ) \left (x -3\right )} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 24

DSolve[{((2*x-1)*(y[x]-1))+((x+2)*(x-3))*D[y[x],x]==0,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2-x+6}{x^2-x-6} \]