# differential equation help for old time learner please !!!

• June 12th 2011, 03:30 AM
oldboy26
differential equation help for old time learner please !!!
hi i have been out of education for quite a while now and im trying to get back into the swing of maths and such since im starting a engineering degree in september and havent been doing much maths since my national certificate years ago now .. im strugling with findind the particular solutions for differential equation. could some one please talk me through this question and the stages i would take to come to the final answer thankyou Bill .

4 d^2 y/ dx^2 + 12 dy/dx +9y = 0 given y=2 and dy/dx=1 at x=0

much apriciated if some maths wiz could help me out :) thanks
• June 12th 2011, 03:35 AM
mr fantastic
Quote:

Originally Posted by oldboy26
hi i have been out of education for quite a while now and im trying to get back into the swing of maths and such since im starting a engineering degree in september and havent been doing much maths since my national certificate years ago now .. im strugling with findind the particular solutions for differential equation. could some one please talk me through this question and the stages i would take to come to the final answer thankyou Bill .

4 d^2 y/ dx^2 + 12 dy/dx +9y = 0 given y=2 and dy/dx=1 at x=0

much apriciated if some maths wiz could help me out :) thanks

The characteristic equation is $\displaystyle 4m^2 + 12m + 9 = 0$
The solution of the DE is $\displaystyle y = C_1e^{m_1 x} + C_2e^{m_2 x}$, where $\displaystyle m_1, m_2$ are the solutions to the characteristic equation.