4.10.39 \((-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2\)

ODE
\[ (-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2 \] ODE Classification

[[_homogeneous, `class C`], _exact, _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 = 0.010106 (sec), leaf count = 71

\[\left \{\left \{y(x)\to \frac {1}{4} \left (-i \sqrt {-16 c_1+19 x^2-14 x-25}+3 x+5\right )\right \},\left \{y(x)\to \frac {1}{4} \left (i \sqrt {-16 c_1+19 x^2-14 x-25}+3 x+5\right )\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 50

\[ \left \{ -{\frac {1}{2}\ln \left ({\frac {1444\, \left (y \relax (x ) \right ) ^{2}+ \left (-2166\,x-3610 \right ) y \relax (x ) +2527\,{x}^{2}+1444\,x+2489}{ \left (-7+19\,x \right ) ^{2}}} \right ) }-\ln \left (-7+19\,x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[(5 + 3*x - 4*y[x])*y'[x] == 2 + 7*x - 3*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (5 + 3*x - I*Sqrt[-25 - 14*x + 19*x^2 - 16*C[1]])/4}, {y[x] -> (5 + 3*
x + I*Sqrt[-25 - 14*x + 19*x^2 - 16*C[1]])/4}}

Maple raw input

dsolve((5+3*x-4*y(x))*diff(y(x),x) = 2+7*x-3*y(x), y(x),'implicit')

Maple raw output

-1/2*ln((1444*y(x)^2+(-2166*x-3610)*y(x)+2527*x^2+1444*x+2489)/(-7+19*x)^2)-ln(-
7+19*x)-_C1 = 0