ODE No. 1466

\[ a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)-e^{a x}+y^{(3)}(x)=0 \]

✓ Mathematica : cpu = 0.0151017 (sec), leaf count = 46

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

\[\left \{\left \{y(x)\to \frac {1}{6} x^3 e^{a x}+c_3 x^2 e^{a x}+c_2 x e^{a x}+c_1 e^{a x}\right \}\right \}\]

✓ Maple : cpu = 0.024 (sec), leaf count = 27

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

\[y \left (x \right ) = \frac {{\mathrm e}^{a x} \left (6 c_{3} x^{2}+x^{3}+6 c_{2} x +6 c_{1} \right )}{6}\]