Internal problem ID [14410]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {1536 x^{9}-34560 x^{8}+345600 x^{7}-2016000 x^{6}+7560000 x^{5}-18900000 x^{4}+31500000 x^{3}+\left (2 c_{1} -28303968\right ) x^{2}+\left (-4 c_{1} +10201686\right ) x +2 c_{1} -413343}{2 \left (2 x -5\right )^{9}} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 82
DSolve[y'[x]==((4-7*x)*(2*y[x]-3))/((x-1)*(2*x-5)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1536 x^9-34560 x^8+345600 x^7-2016000 x^6+7560000 x^5-18900000 x^4+31500000 x^3-2 (16402608+c_1) x^2+2 (9602091+2 c_1) x-4914591-2 c_1}{2 (2 x-5)^9} \\ y(x)\to \frac {3}{2} \\ \end{align*}