# Solve the following differential eqn with constant variables

In this image you can see an Ex 3 I have formed the auxilary Eqn i, but i am not able to solve the auxilary eqn with degree 4 , and find the roots of the eqn

• There are "obvious" roots to $m^4-m^3-9 m^2-11 m-4=0$; at least, $m=-1$ is a double root. Just continue ! – Claude Leibovici May 6 '17 at 5:02
• @projectilemotion. I know that; I just wanted the user to finish the work ! Cheers. – Claude Leibovici May 6 '17 at 6:04

## 1 Answer

Notice that at one point during your calculations, you somehow 'converted' a minus sign into a plus sign. Your auxilliary equation should be: $$m^4-m^3-9m^2-11m\color{red}{-}4=0$$ Using the Rational Root Theorem, we know that $m=4$ is a solution to your auxilliary equation.

Using polynomial division, we obtain: $$\frac{m^4-m^3-9m^2-11m-4}{m-4}=m^3+3m^2+3m+1, m\neq 4$$ Notice that this may be factored to give $(m+1)^3$. Hence, $m=-1$ is a root of multiplicity $3$.

Can you continue, and find the general solution from this?

• Thnku so much @projectilemotion's 😊 – Akshie Dhiman May 6 '17 at 8:10