Internal problem ID [11685]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {2 x -7 y}{3 y-8 x}=0} \]
✓ Solution by Maple
Time used: 0.032 (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 \left (x \right ) &= \frac {-12 c_{1} x -\sqrt {-60 c_{1} x +1}+1}{18 c_{1}} \\ y \left (x \right ) &= \frac {-12 c_{1} x +1+\sqrt {-60 c_{1} x +1}}{18 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.969 (sec). Leaf size: 80
DSolve[y'[x]==(2*x-7*y[x])/(3*y[x]-8*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{18} \left (-12 x-e^{\frac {c_1}{2}} \sqrt {60 x+e^{c_1}}-e^{c_1}\right ) \\ y(x)\to \frac {1}{18} \left (-12 x+e^{\frac {c_1}{2}} \sqrt {60 x+e^{c_1}}-e^{c_1}\right ) \\ \end{align*}