# Third order differential equation with constant coefficient

My problem is: Solve the initial value problem $(D^3-4D^2+4D-4)y=0$ where $D=\frac{d}{dx}$ y(0)=y'(0)=2, y''(0)=0 and find the value of $y(\pi/2)$ I know that it can be solved by considering complementary function. But I am unable to find the roots ( without using calculator). I even tried to solve it by Taylor method but couldn't get the Answer. Any help will be appreciated. Thank in advance.

• It is nasty and this is no better than a numerical approach: en.wikipedia.org/wiki/Cubic_function – Moo Apr 20 '16 at 7:04
• If it is a training exercise, probably there is a typo. – JJacquelin Apr 20 '16 at 8:25