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]