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 = 0.181201 (sec), leaf count = 71
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right )\right \},\left \{y(x)\to \frac {1}{4} \left (i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right )\right \}\right \}\]
Maple ✓
cpu = 0.191 (sec), leaf count = 38
\[\left [y \left (x \right ) = \frac {29}{19}-\frac {-\frac {3 \left (-7+19 x \right ) \textit {\_C1}}{2}+\frac {\sqrt {-19 \left (-7+19 x \right )^{2} \textit {\_C1}^{2}+4}}{2}}{38 \textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = 29/19-1/38*(-3/2*(-7+19*x)*_C1+1/2*(-19*(-7+19*x)^2*_C1^2+4)^(1/2))/_C1]