ODE
\[ y''(x)=e^x x \] ODE Classification
[[_2nd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0069149 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2 x+c_1+e^x (x-2)\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) = \left ( x-2 \right ) {{\rm e}^{x}}+{\it \_C1}\,x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[y''[x] == E^x*x,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(-2 + x) + C[1] + x*C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = x*exp(x), y(x),'implicit')
Maple raw output
y(x) = (x-2)*exp(x)+_C1*x+_C2