Show that the equation f''(x) + 4f'(x) + 4f(x) = 0
is satisfied if f(x) = (3x-5)e^-2x (thats e to the power of -2x, not e to the power of -2 times x)
any help would be greatly appreciated. can't seem to get it to equal 0
Initial equation
First derivative, remember to use the chain rule and the multiplication rule. The multiplication rule says that the derivative of f(x)g(x) is f'(x)g(x)+g'(x)f(x). And the chain rule in this case says the derivative of is which becomes
Second derivative, remember the same rules.
Now just plug them into the equation
and simplify