Find the general solution of the second-order, linear, homogeneous differential equation 4y′′− 20y′ + 25y = 0.
I have got up to the stage where I have found landa to be =5/2 but do not know what to do after that. Please help.
Find the general solution of the second-order, linear, homogeneous differential equation 4y′′− 20y′ + 25y = 0.
I have got up to the stage where I have found landa to be =5/2 but do not know what to do after that. Please help.
If $\displaystyle y = e^{mx}$ then $\displaystyle 4m^2-20m+25 = 0$ and as you said $\displaystyle m = \frac{5}{2}, \frac{5}{2}$. Sicne the root is repeated the the two solutions are
$\displaystyle y_1 = e^{\frac{5x}{2}},\;\;\;y_2 = x\,e^{\frac{5x}{2}} $
and the general solution solution
$\displaystyle y = c_1 e^{\frac{5x}{2}} + c_2 x\,e^{\frac{5x}{2}} $