Internal problem ID [11694]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {2 x +7 y}{-2 y+2 x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 18
dsolve([diff(y(x),x)=(2*x+7*y(x))/(2*x-2*y(x)),y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 \sqrt {16-15 x}}{5}-2 x +\frac {16}{5} \]
✓ Solution by Mathematica
Time used: 1.383 (sec). Leaf size: 25
DSolve[{y'[x]==(2*x+7*y[x])/(2*x-2*y[x]),{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2}{5} \left (-5 x+2 \sqrt {16-15 x}+8\right ) \]