74.8.8 problem 8

Internal problem ID [16144]
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 : Tuesday, January 28, 2025 at 08:51:55 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==((4-7*x)*(2*y[x]-3))/((x-1)*(2*x-5)),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*}