74.8.8 problem 8

Internal problem ID [16065]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 8
Date solved : Thursday, March 13, 2025 at 07:38:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 69

ode:=diff(y(x),x) = (4-7*x)*(2*y(x)-3)/(x-1)/(2*x-5); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1536 x^{9}-34560 x^{8}+345600 x^{7}-2016000 x^{6}+7560000 x^{5}-18900000 x^{4}[phone] x^{3}+\left (2 c_{1} -28303968\right ) x^{2}+\left (-4 c_{1} [phone]\right ) x +2 c_{1} -413343}{2 \left (2 x -5\right )^{9}} \]

✓ Mathematica. Time used: 0.255 (sec). Leaf size: 108

ode=D[y[x],x]==((4-7*x)*(2*y[x]-3))/((x-1)*(2*x-5)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \exp \left (\int _1^x\frac {8-14 K[1]}{2 K[1]^2-7 K[1]+5}dK[1]\right ) \left (\int _1^x\frac {3 \exp \left (-\int _1^{K[2]}\frac {8-14 K[1]}{2 K[1]^2-7 K[1]+5}dK[1]\right ) (7 K[2]-4)}{2 K[2]^2-7 K[2]+5}dK[2]+c_1\right ) \\ y(x)\to \frac {3}{2} \\ \end{align*}

✓ Sympy. Time used: 0.655 (sec). Leaf size: 168

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(4 - 7*x)*(2*y(x) - 3)/((x - 1)*(2*x - 5)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {256 x^{2} e^{2 C_{1}}}{512 x^{9} - 11520 x^{8} + 115200 x^{7} - 672000 x^{6} + 2520000 x^{5} - 6300000 x^{4} + 10500000 x^{3} - 11250000 x^{2} + 7031250 x - 1953125} - \frac {512 x e^{2 C_{1}}}{512 x^{9} - 11520 x^{8} + 115200 x^{7} - 672000 x^{6} + 2520000 x^{5} - 6300000 x^{4} + 10500000 x^{3} - 11250000 x^{2} + 7031250 x - 1953125} + \frac {3}{2} + \frac {256 e^{2 C_{1}}}{512 x^{9} - 11520 x^{8} + 115200 x^{7} - 672000 x^{6} + 2520000 x^{5} - 6300000 x^{4} + 10500000 x^{3} - 11250000 x^{2} + 7031250 x - 1953125} \]