Originally Posted by
algorithm Hello,
Second order differential equation:
y'' - y = exp[x]
Solving for the complementary function, y_c:
m^2 - 1 = 0
-> m = 1 and m = 0 (*)
:. y_c = A*exp[-1] + B*exp[0] = A*exp[-1] + B (**)
Solving for the particular integral, y_p:
Try y = a*exp[x] -> this is a solution of the homogeneous eqn, so multiply the function by x:
y = ax*exp[x]
y' = a*exp[x] + ax*exp[x]
y'' = a*exp[x] + a*exp[x] + ax*exp[x]
Substituting into y'' - y' = x*exp[x], (***) the equation reduces to:
a + a*x = x -> How to work the constant (alpha) out?
Thank you