64.6.11 problem 11

Internal problem ID [13361]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 05:32:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \end{align*}

✓ Solution by Maple

Time used: 0.111 (sec). Leaf size: 47

dsolve(diff(y(x),x)=(2*x-7*y(x))/(3*y(x)-8*x),y(x), singsol=all)
 

\begin{align*} y &= \frac {-12 c_{1} x -\sqrt {-60 c_{1} x +1}+1}{18 c_{1}} \\ y &= \frac {-12 c_{1} x +1+\sqrt {-60 c_{1} x +1}}{18 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 44

DSolve[D[y[x],x]==(2*x-7*y[x])/(3*y[x]-8*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {3 K[1]-8}{(K[1]-1) (3 K[1]+2)}dK[1]=-\log (x)+c_1,y(x)\right ] \]