4.36.50 $y^{″}(x)=a+4b^{2}y(x)+3by(x{)}^2+3y(x)y^{\prime }(x)$

ODE
$$y^{″}(x)=a+4b^{2}y(x)+3by(x{)}^2+3y(x)y^{\prime }(x)$$ ODE Classification

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica ✓
cpu = 10.979 (sec), leaf count = 2742

$$\left\{\{y(x)\to \frac{-i^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{2}^{\frac{3(b^3+\sqrt{4b^6-3a{b}^3})}{2b^3}}{3}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{a}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{b}^{\frac{\sqrt{4b^6-3a{b}^3}}{b^3}+3}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{I}_{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)\mathrm{\Gamma }(\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1)c_1^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}+i^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{2}^{\frac{3\sqrt{4b^6-3a{b}^3}}{2b^3}+\frac{1}{2}}{3}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{a}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{b}^{\frac{\sqrt{4b^6-3a{b}^3}}{b^3}+\frac{3}{2}}\sqrt{4b^3-3a}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{I}_{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)\mathrm{\Gamma }(\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1)c_1^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}-i^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{2}^{\frac{3\sqrt{4b^6-3a{b}^3}}{2b^3}+\frac{1}{2}}{3}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{a}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{b}^{\frac{\sqrt{4b^6-3a{b}^3}}{b^3}}\sqrt{4b^6-3a{b}^3}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{I}_{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)\mathrm{\Gamma }(\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1)c_1^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}+2^{\frac{3\sqrt{4b^3-3a}}{2b^{3/2}}+\frac{1}{2}}{3}^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}{a}^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}{b}^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}(-2b^3-\sqrt{4b^3-3a}{b}^{3/2}+\sqrt{4b^6-3a{b}^3}){\left(\frac{e^{-2bx}}{a}\right)}^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}{I}_{-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)c_2\mathrm{\Gamma }(1-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3})c_1^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}+i^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{2}^{\frac{3\sqrt{4b^6-3a{b}^3}}{2b^3}}{3}^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}{a}^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}{b}^{\frac{\sqrt{4b^6-3a{b}^3}}{b^3}+2}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}{I}_{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}-1}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)\mathrm{\Gamma }(\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1)c_1^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}+i^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{2}^{\frac{3\sqrt{4b^6-3a{b}^3}}{2b^3}}{3}^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}{a}^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}{b}^{\frac{\sqrt{4b^6-3a{b}^3}}{b^3}+2}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}{I}_{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)\mathrm{\Gamma }(\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1)c_1^{\frac{1}{2}(\frac{\sqrt{4b^3-3a}}{b^{3/2}}+1)}+2^{\frac{3\sqrt{4b^3-3a}}{2b^{3/2}}}{3}^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}{a}^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}{b}^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}+2}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}{I}_{-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}-1}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)c_2\mathrm{\Gamma }(1-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3})c_1^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}+2^{\frac{3\sqrt{4b^3-3a}}{2b^{3/2}}}{3}^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}{a}^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}{b}^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}+2}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}{I}_{1-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)c_2\mathrm{\Gamma }(1-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3})c_1^{\frac{b^3+\sqrt{4b^6-3a{b}^3}}{2b^3}}}{3\sqrt{2}{b}^2(i^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{2}^{\frac{3\sqrt{4b^6-3a{b}^3}}{2b^3}}{3}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{a}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{b}^{\frac{\sqrt{4b^6-3a{b}^3}}{b^3}}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}{I}_{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)\mathrm{\Gamma }(\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}+1)c_1^{\frac{\sqrt{4b^3-3a}}{2b^{3/2}}}+2^{\frac{3\sqrt{4b^3-3a}}{2b^{3/2}}}{3}^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}{a}^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}{b}^{\frac{\sqrt{4b^3-3a}}{b^{3/2}}}{\left(\frac{e^{-2bx}}{a}\right)}^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}{I}_{-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}}\left(\frac{\sqrt{\frac{3}{2}}\sqrt{a}\sqrt{\frac{e^{-2bx}}{a}}\sqrt{c_1}}{b}\right)c_2\mathrm{\Gamma }(1-\frac{\sqrt{4b^6-3a{b}^3}}{2b^3})c_1^{\frac{\sqrt{4b^6-3a{b}^3}}{2b^3}})}\}\right\}$$

Maple ✓
cpu = 0.646 (sec), leaf count = 849

$$\{{\int }^{y\left(x\right)}-2b^2{(-4\mathit{\_}\mathit{a}{b}^3-3b^2{\mathit{\_}\mathit{a}}^2+{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(6{\mathit{K}}_{1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})\mathit{\_}\mathit{C}\mathit{1}{b}^2+9{\mathit{K}}_{1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})\mathit{\_}\mathit{C}\mathit{1}b\mathit{\_}\mathit{a}-3\sqrt{4b^4-3ab}{\mathit{K}}_{1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})\mathit{\_}\mathit{C}\mathit{1}+3{\mathit{K}}_{1/2\frac{4b^3+2\sqrt{4b^4-3ab}b-3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}+6{\mathit{I}}_{-1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})b^2+9{\mathit{I}}_{-1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})b\mathit{\_}\mathit{a}-3{\mathit{I}}_{1/2\frac{4b^3+2\sqrt{4b^4-3ab}b-3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2})\sqrt{3}\mathit{\_}\mathit{Z}-3\sqrt{4b^4-3ab}{\mathit{I}}_{-1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}(-1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}))\right)}^2-ab)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-2b^2{(-4\mathit{\_}\mathit{a}{b}^3-3b^2{\mathit{\_}\mathit{a}}^2+{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(6{\mathit{K}}_{1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)\mathit{\_}\mathit{C}\mathit{1}{b}^2+9{\mathit{K}}_{1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)\mathit{\_}\mathit{C}\mathit{1}b\mathit{\_}\mathit{a}-3\sqrt{4b^4-3ab}{\mathit{K}}_{1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)\mathit{\_}\mathit{C}\mathit{1}+3{\mathit{K}}_{1/2\frac{4b^3+2\sqrt{4b^4-3ab}b-3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}+6{\mathit{I}}_{-1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)b^2+9{\mathit{I}}_{-1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)b\mathit{\_}\mathit{a}-3{\mathit{I}}_{1/2\frac{4b^3+2\sqrt{4b^4-3ab}b-3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right)\sqrt{3}\mathit{\_}\mathit{Z}-3\sqrt{4b^4-3ab}{\mathit{I}}_{-1/2\frac{-4b^3+3a}{\sqrt{4b^4-3ab}b}}\left(1/2\frac{\sqrt{3}\mathit{\_}\mathit{Z}}{b^2}\right))\right)}^2-ab)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$ Mathematica raw input

DSolve[y''[x] == a + 4*b^2*y[x] + 3*b*y[x]^2 + 3*y[x]*y'[x],y[x],x]

Mathematica raw output

{{y[x] -> (2^(1/2 + (3*Sqrt[-3*a + 4*b^3])/(2*b^(3/2)))*3^(Sqrt[-3*a*b^3 + 4*b^6
]/(2*b^3))*a^(Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3))*b^(Sqrt[-3*a + 4*b^3]/b^(3/2))*(-2
*b^3 - b^(3/2)*Sqrt[-3*a + 4*b^3] + Sqrt[-3*a*b^3 + 4*b^6])*(1/(a*E^(2*b*x)))^(S
qrt[-3*a*b^3 + 4*b^6]/(2*b^3))*BesselI[-Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/
2]*Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^(Sqrt[-3*a*b^3 + 4*b^6]/(2*
b^3))*C[2]*Gamma[1 - Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)] + 2^((3*Sqrt[-3*a + 4*b^3])
/(2*b^(3/2)))*3^((b^3 + Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*a^((b^3 + Sqrt[-3*a*b^3
 + 4*b^6])/(2*b^3))*b^(2 + Sqrt[-3*a + 4*b^3]/b^(3/2))*(1/(a*E^(2*b*x)))^((b^3 +
 Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*BesselI[-1 - Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (
Sqrt[3/2]*Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^((b^3 + Sqrt[-3*a*b^
3 + 4*b^6])/(2*b^3))*C[2]*Gamma[1 - Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)] + 2^((3*Sqrt
[-3*a + 4*b^3])/(2*b^(3/2)))*3^((b^3 + Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*a^((b^3 
+ Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*b^(2 + Sqrt[-3*a + 4*b^3]/b^(3/2))*(1/(a*E^(2
*b*x)))^((b^3 + Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*BesselI[1 - Sqrt[-3*a*b^3 + 4*b
^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^((b^3 
+ Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*C[2]*Gamma[1 - Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)
] - I^(Sqrt[-3*a + 4*b^3]/b^(3/2))*2^((3*(b^3 + Sqrt[-3*a*b^3 + 4*b^6]))/(2*b^3)
)*3^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*a^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*b^(3 + S
qrt[-3*a*b^3 + 4*b^6]/b^3)*(1/(a*E^(2*b*x)))^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*Be
sselI[Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*S
qrt[C[1]])/b]*C[1]^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*Gamma[1 + Sqrt[-3*a*b^3 + 4*
b^6]/(2*b^3)] + I^(Sqrt[-3*a + 4*b^3]/b^(3/2))*2^(1/2 + (3*Sqrt[-3*a*b^3 + 4*b^6
])/(2*b^3))*3^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*a^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2))
)*b^(3/2 + Sqrt[-3*a*b^3 + 4*b^6]/b^3)*Sqrt[-3*a + 4*b^3]*(1/(a*E^(2*b*x)))^(Sqr
t[-3*a + 4*b^3]/(2*b^(3/2)))*BesselI[Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/2]*
Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)
))*Gamma[1 + Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)] - I^(Sqrt[-3*a + 4*b^3]/b^(3/2))*2^
(1/2 + (3*Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*3^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*a^
(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*b^(Sqrt[-3*a*b^3 + 4*b^6]/b^3)*Sqrt[-3*a*b^3 + 
4*b^6]*(1/(a*E^(2*b*x)))^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*BesselI[Sqrt[-3*a*b^3 
+ 4*b^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^(
Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*Gamma[1 + Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)] + I^(S
qrt[-3*a + 4*b^3]/b^(3/2))*2^((3*Sqrt[-3*a*b^3 + 4*b^6])/(2*b^3))*3^((1 + Sqrt[-
3*a + 4*b^3]/b^(3/2))/2)*a^((1 + Sqrt[-3*a + 4*b^3]/b^(3/2))/2)*b^(2 + Sqrt[-3*a
*b^3 + 4*b^6]/b^3)*(1/(a*E^(2*b*x)))^((1 + Sqrt[-3*a + 4*b^3]/b^(3/2))/2)*Bessel
I[-1 + Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a]*Sqrt[1/(a*E^(2*b*x))]*
Sqrt[C[1]])/b]*C[1]^((1 + Sqrt[-3*a + 4*b^3]/b^(3/2))/2)*Gamma[1 + Sqrt[-3*a*b^3
 + 4*b^6]/(2*b^3)] + I^(Sqrt[-3*a + 4*b^3]/b^(3/2))*2^((3*Sqrt[-3*a*b^3 + 4*b^6]
)/(2*b^3))*3^((1 + Sqrt[-3*a + 4*b^3]/b^(3/2))/2)*a^((1 + Sqrt[-3*a + 4*b^3]/b^(
3/2))/2)*b^(2 + Sqrt[-3*a*b^3 + 4*b^6]/b^3)*(1/(a*E^(2*b*x)))^((1 + Sqrt[-3*a + 
4*b^3]/b^(3/2))/2)*BesselI[1 + Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a
]*Sqrt[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^((1 + Sqrt[-3*a + 4*b^3]/b^(3/2))/2)
*Gamma[1 + Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)])/(3*Sqrt[2]*b^2*(2^((3*Sqrt[-3*a + 4*
b^3])/(2*b^(3/2)))*3^(Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3))*a^(Sqrt[-3*a*b^3 + 4*b^6]/
(2*b^3))*b^(Sqrt[-3*a + 4*b^3]/b^(3/2))*(1/(a*E^(2*b*x)))^(Sqrt[-3*a*b^3 + 4*b^6
]/(2*b^3))*BesselI[-Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a]*Sqrt[1/(a
*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^(Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3))*C[2]*Gamma[1 -
 Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)] + I^(Sqrt[-3*a + 4*b^3]/b^(3/2))*2^((3*Sqrt[-3*
a*b^3 + 4*b^6])/(2*b^3))*3^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*a^(Sqrt[-3*a + 4*b^3
]/(2*b^(3/2)))*b^(Sqrt[-3*a*b^3 + 4*b^6]/b^3)*(1/(a*E^(2*b*x)))^(Sqrt[-3*a + 4*b
^3]/(2*b^(3/2)))*BesselI[Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3), (Sqrt[3/2]*Sqrt[a]*Sqrt
[1/(a*E^(2*b*x))]*Sqrt[C[1]])/b]*C[1]^(Sqrt[-3*a + 4*b^3]/(2*b^(3/2)))*Gamma[1 +
 Sqrt[-3*a*b^3 + 4*b^6]/(2*b^3)]))}}

Maple raw input

dsolve(diff(diff(y(x),x),x) = 3*y(x)*diff(y(x),x)+a+4*b^2*y(x)+3*b*y(x)^2, y(x),'implicit')

Maple raw output

Intat(-2/(-4*_a*b^3-3*b^2*_a^2+RootOf(6*BesselK(1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(
1/2)/b,-1/2/b^2*3^(1/2)*_Z)*_C1*b^2+9*BesselK(1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/
2)/b,-1/2/b^2*3^(1/2)*_Z)*_C1*b*_a-3*(4*b^4-3*a*b)^(1/2)*BesselK(1/2*(-4*b^3+3*a
)/(4*b^4-3*a*b)^(1/2)/b,-1/2/b^2*3^(1/2)*_Z)*_C1+3*BesselK(1/2*(4*b^3+2*(4*b^4-3
*a*b)^(1/2)*b-3*a)/(4*b^4-3*a*b)^(1/2)/b,-1/2/b^2*3^(1/2)*_Z)*3^(1/2)*_C1*_Z+6*B
esselI(-1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/b,-1/2/b^2*3^(1/2)*_Z)*b^2+9*Bessel
I(-1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/b,-1/2/b^2*3^(1/2)*_Z)*b*_a-3*BesselI(1/
2*(4*b^3+2*(4*b^4-3*a*b)^(1/2)*b-3*a)/(4*b^4-3*a*b)^(1/2)/b,-1/2/b^2*3^(1/2)*_Z)
*3^(1/2)*_Z-3*(4*b^4-3*a*b)^(1/2)*BesselI(-1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/
b,-1/2/b^2*3^(1/2)*_Z))^2-a*b)*b^2,_a = y(x))-x-_C2 = 0, Intat(-2/(-4*_a*b^3-3*b
^2*_a^2+RootOf(6*BesselK(1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*
_Z)*_C1*b^2+9*BesselK(1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*_Z)
*_C1*b*_a-3*(4*b^4-3*a*b)^(1/2)*BesselK(1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/b,1
/2/b^2*3^(1/2)*_Z)*_C1+3*BesselK(1/2*(4*b^3+2*(4*b^4-3*a*b)^(1/2)*b-3*a)/(4*b^4-
3*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*_Z)*3^(1/2)*_C1*_Z+6*BesselI(-1/2*(-4*b^3+3*a)/(4
*b^4-3*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*_Z)*b^2+9*BesselI(-1/2*(-4*b^3+3*a)/(4*b^4-3
*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*_Z)*b*_a-3*BesselI(1/2*(4*b^3+2*(4*b^4-3*a*b)^(1/2
)*b-3*a)/(4*b^4-3*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*_Z)*3^(1/2)*_Z-3*(4*b^4-3*a*b)^(1
/2)*BesselI(-1/2*(-4*b^3+3*a)/(4*b^4-3*a*b)^(1/2)/b,1/2/b^2*3^(1/2)*_Z))^2-a*b)*
b^2,_a = y(x))-x-_C2 = 0