4.21.44 $y^{\prime }(x{)}^3+e^{3x-2y(x)}(y^{\prime }(x)-1)=0$

ODE
$$y^{\prime }(x{)}^3+e^{3x-2y(x)}(y^{\prime }(x)-1)=0$$ ODE Classification

[[_homogeneous, `class C`], _dAlembert]

Book solution method
Change of variable

Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 284.418 (sec), leaf count = 514

$$\{x+6{\int }^{-3/2x+y\left(x\right)}\frac{{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}}}{3i{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{2{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+3{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+27{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}\sqrt[6]{3}+3i{\mathrm{e}}^3\sqrt[6]{3}\sqrt[3]{2}-{\mathrm{e}}^3\sqrt[3]{18}+{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{27{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+243{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}+18{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-6{\int }^{-3/2x+y\left(x\right)}\frac{{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}}}{3i{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{2{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+3{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+27{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}\sqrt[6]{3}+3i{\mathrm{e}}^3\sqrt[6]{3}\sqrt[3]{2}+{\mathrm{e}}^3\sqrt[3]{18}-{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{27{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+243{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}+18{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}}-9{\mathrm{e}}^{2\mathit{\_}\mathit{a}+3}\sqrt[3]{\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-6{\int }^{-3/2x+y\left(x\right)}\frac{{\mathrm{e}}^{2\mathit{\_}\mathit{a}}\sqrt[3]{\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}}}{2{\mathrm{e}}^{2\mathit{\_}\mathit{a}}\sqrt[3]{27{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+243{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}+18{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}}-2\sqrt[3]{18}-9{\mathrm{e}}^{2\mathit{\_}\mathit{a}}\sqrt[3]{\sqrt{12{\mathrm{e}}^{-6\mathit{\_}\mathit{a}}+81{\mathrm{e}}^{-4\mathit{\_}\mathit{a}}}+9{\mathrm{e}}^{-2\mathit{\_}\mathit{a}}}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[E^(3*x - 2*y[x])*(-1 + y'[x]) + y'[x]^3 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(diff(y(x),x)^3+exp(3*x-2*y(x))*(diff(y(x),x)-1) = 0, y(x),'implicit')

Maple raw output

x-6*Intat(exp(2*_a)*((12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+9*exp(-2*_a))^(1/3)/(2*
exp(2*_a)*(27*exp(-2*_a)*(12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+243*exp(-4*_a)+18*e
xp(-6*_a))^(1/3)-2*18^(1/3)-9*exp(2*_a)*((12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+9*e
xp(-2*_a))^(1/3)),_a = -3/2*x+y(x))-_C1 = 0, x+6*Intat(((12*exp(-6*_a)+81*exp(-4
*_a))^(1/2)+9*exp(-2*_a))^(1/3)/(3*I*exp(2*_a+3)*(2*exp(-6*_a)+3*exp(-2*_a)*(12*
exp(-6*_a)+81*exp(-4*_a))^(1/2)+27*exp(-4*_a))^(1/3)*3^(1/6)+3*I*exp(3)*3^(1/6)*
2^(1/3)-exp(3)*18^(1/3)+exp(2*_a+3)*(27*exp(-2*_a)*(12*exp(-6*_a)+81*exp(-4*_a))
^(1/2)+243*exp(-4*_a)+18*exp(-6*_a))^(1/3)+9*exp(2*_a+3)*((12*exp(-6*_a)+81*exp(
-4*_a))^(1/2)+9*exp(-2*_a))^(1/3))*exp(2*_a+3),_a = -3/2*x+y(x))-_C1 = 0, x-6*In
tat(((12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+9*exp(-2*_a))^(1/3)/(3*I*exp(2*_a+3)*(2
*exp(-6*_a)+3*exp(-2*_a)*(12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+27*exp(-4*_a))^(1/3
)*3^(1/6)+3*I*exp(3)*3^(1/6)*2^(1/3)+exp(3)*18^(1/3)-exp(2*_a+3)*(27*exp(-2*_a)*
(12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+243*exp(-4*_a)+18*exp(-6*_a))^(1/3)-9*exp(2*
_a+3)*((12*exp(-6*_a)+81*exp(-4*_a))^(1/2)+9*exp(-2*_a))^(1/3))*exp(2*_a+3),_a =
 -3/2*x+y(x))-_C1 = 0