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 = 0.129511 (sec), leaf count = 256

\[\left \{\left \{y(x)\to \frac {1}{2} \left (\frac {(10-10 i) (x+3)}{\frac {i \sqrt {2}}{\sqrt {(x+3) \sinh \left (\frac {2 c_1}{9}\right )+(x+3) \cosh \left (\frac {2 c_1}{9}\right )-i}}+(1-i)}-9 x-19\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {(10-10 i) (x+3)}{(1-i)-\frac {i \sqrt {2}}{\sqrt {(x+3) \sinh \left (\frac {2 c_1}{9}\right )+(x+3) \cosh \left (\frac {2 c_1}{9}\right )-i}}}-9 x-19\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {(10-10 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {(x+3) \sinh \left (\frac {2 c_1}{9}\right )+(x+3) \cosh \left (\frac {2 c_1}{9}\right )+i}}}-9 x-19\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {(10-10 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {(x+3) \sinh \left (\frac {2 c_1}{9}\right )+(x+3) \cosh \left (\frac {2 c_1}{9}\right )+i}}+(1-i)}-9 x-19\right )\right \}\right \}\]

Maple
cpu = 0.031 (sec), leaf count = 45

\[ \left \{ \ln \left ({\frac {-y \relax (x ) -2-2\,x}{3+x}} \right ) -2\,\ln \left ({\frac {11+x-2\,y \relax (x ) }{3+x}} \right ) -\ln \left (3+x \right ) -{\it \_C1}=0 \right \} \] 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 - 9*x + ((10 - 10*I)*(3 + x))/((1 - I) + (I*Sqrt[2])/Sqrt[-I + (3
 + x)*Cosh[(2*C[1])/9] + (3 + x)*Sinh[(2*C[1])/9]]))/2}, {y[x] -> (-19 - 9*x + (
(10 - 10*I)*(3 + x))/((1 - I) - (I*Sqrt[2])/Sqrt[-I + (3 + x)*Cosh[(2*C[1])/9] +
 (3 + x)*Sinh[(2*C[1])/9]]))/2}, {y[x] -> (-19 - 9*x + ((10 - 10*I)*(3 + x))/((1
 - I) - Sqrt[2]/Sqrt[I + (3 + x)*Cosh[(2*C[1])/9] + (3 + x)*Sinh[(2*C[1])/9]]))/
2}, {y[x] -> (-19 - 9*x + ((10 - 10*I)*(3 + x))/((1 - I) + Sqrt[2]/Sqrt[I + (3 +
 x)*Cosh[(2*C[1])/9] + (3 + x)*Sinh[(2*C[1])/9]]))/2}}

Maple raw input

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

Maple raw output

ln((-y(x)-2-2*x)/(3+x))-2*ln((11+x-2*y(x))/(3+x))-ln(3+x)-_C1 = 0