##### 4.10.25 $$(2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0$$

ODE
$(2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0$ ODE Classiﬁcation

[[_homogeneous, class C], _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 = 0.352577 (sec), leaf count = 256

$\left \{\left \{y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}+(1-i)}-\frac {19}{2}\right \},\left \{y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}}-\frac {19}{2}\right \},\left \{y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}}-\frac {19}{2}\right \},\left \{y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}+(1-i)}-\frac {19}{2}\right \}\right \}$

Maple
cpu = 0.06 (sec), leaf count = 29

$\left [y \left (x \right ) = 4+\frac {4 \left (3+x \right ) \textit {\_C1} +\sqrt {-40 \left (3+x \right ) \textit {\_C1} +1}-1}{8 \textit {\_C1}}\right ]$ Mathematica raw input

DSolve[18 - 2*x - 6*y[x] + (19 + 9*x + 2*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -19/2 - (9*x)/2 + ((5 - 5*I)*(3 + x))/((1 - I) + (I*Sqrt[2])/Sqrt[-I +
 (3 + x)*Cosh[(2*C[1])/9] + (3 + x)*Sinh[(2*C[1])/9]])}, {y[x] -> -19/2 - (9*x)/
2 + ((5 - 5*I)*(3 + x))/((1 - I) - (I*Sqrt[2])/Sqrt[-I + (3 + x)*Cosh[(2*C[1])/9
] + (3 + x)*Sinh[(2*C[1])/9]])}, {y[x] -> -19/2 - (9*x)/2 + ((5 - 5*I)*(3 + x))/
((1 - I) - Sqrt[2]/Sqrt[I + (3 + x)*Cosh[(2*C[1])/9] + (3 + x)*Sinh[(2*C[1])/9]]
)}, {y[x] -> -19/2 - (9*x)/2 + ((5 - 5*I)*(3 + x))/((1 - I) + Sqrt[2]/Sqrt[I + (
3 + x)*Cosh[(2*C[1])/9] + (3 + x)*Sinh[(2*C[1])/9]])}}

Maple raw input

dsolve((19+9*x+2*y(x))*diff(y(x),x)+18-2*x-6*y(x) = 0, y(x))

Maple raw output

[y(x) = 4+1/8*(4*(3+x)*_C1+(-40*(3+x)*_C1+1)^(1/2)-1)/_C1]