89.8.17 problem 19

Internal problem ID [24477]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 66
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:41:18 PM
CAS classification : [_linear]

\begin{align*} 2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 26

ode:=2*x-3*y(x)+4+3*(x-1)*diff(y(x),x) = 0; 
ic:=[y(3) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (-2 x +2\right ) \ln \left (x -1\right )}{3}+2+\frac {\left (2 x -2\right ) \ln \left (2\right )}{3} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 28

ode=(2*x-3*y[x]+4 )+3*(x-1 )*D[y[x],x]==0; 
ic={y[3]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{3} (x \log (2)-(x-1) \log (x-1)+3-\log (2)) \end{align*}

✓ Sympy. Time used: 0.195 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (3*x - 3)*Derivative(y(x), x) - 3*y(x) + 4,0) 
ics = {y(3): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {2 x \log {\left (x - 1 \right )}}{3} + \frac {2 x \log {\left (2 \right )}}{3} + \frac {2 \log {\left (x - 1 \right )}}{3} - \frac {2 \log {\left (2 \right )}}{3} + 2 \]