4.10.6 \((4 x-y(x)) y'(x)-5 y(x)+2 x=0\)

ODE
\[ (4 x-y(x)) y'(x)-5 y(x)+2 x=0 \] ODE Classification

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type``class A`]]

Book solution method
Equation linear in the variables, \(y'(x)=f\left (\frac {X_1}{X_2} \right ) \)

Mathematica
cpu = 0.0349802 (sec), leaf count = 80

\[\left \{\left \{y(x)\to \frac {1}{2} \left (-e^{\frac {c_1}{2}} \sqrt {e^{c_1}+12 x}-e^{c_1}-4 x\right )\right \},\left \{y(x)\to \frac {1}{2} \left (e^{\frac {c_1}{2}} \sqrt {e^{c_1}+12 x}-e^{c_1}-4 x\right )\right \}\right \}\]

Maple
cpu = 0.022 (sec), leaf count = 35

\[ \left \{ -2\,\ln \left ({\frac {2\,x+y \relax (x ) }{x}} \right ) +\ln \left ({\frac {y \relax (x ) -x}{x}} \right ) -\ln \relax (x ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[2*x - 5*y[x] + (4*x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-E^C[1] - 4*x - E^(C[1]/2)*Sqrt[E^C[1] + 12*x])/2}, {y[x] -> (-E^C[1]
 - 4*x + E^(C[1]/2)*Sqrt[E^C[1] + 12*x])/2}}

Maple raw input

dsolve((4*x-y(x))*diff(y(x),x)+2*x-5*y(x) = 0, y(x),'implicit')

Maple raw output

-2*ln((2*x+y(x))/x)+ln((y(x)-x)/x)-ln(x)-_C1 = 0