ODE
\[ y''(x)-7 y'(x)+12 y(x)=x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.005434 (sec), leaf count = 30
\[\left \{\left \{y(x)\to c_1 e^{3 x}+c_2 e^{4 x}+\frac {x}{12}+\frac {7}{144}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={{\rm e}^{4\,x}}{\it \_C2}+{{\rm e}^{3\,x}}{\it \_C1}+{\frac {x}{12}}+{\frac {7}{144}} \right \} \] Mathematica raw input
DSolve[12*y[x] - 7*y'[x] + y''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> 7/144 + x/12 + E^(3*x)*C[1] + E^(4*x)*C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-7*diff(y(x),x)+12*y(x) = x, y(x),'implicit')
Maple raw output
y(x) = exp(4*x)*_C2+exp(3*x)*_C1+1/12*x+7/144