Second order linear diffrential equation with constant coeffecient
Download as PPTX, PDF2 likes466 views
The document is a presentation on ordinary and partial differential equations. It summarizes solving a second order linear differential equation with constant coefficients. The equation is 4 d^2y/dx^2 - 2 dy/dx + 5y = 0. Letting y = e^mx, the auxiliary equation is derived as 4m^2 - 2m + 5 = 0. The general solution is found to be y = e^(1/4x) [A cos(76x/8) + B sin(76x/8)].
Second order linear diffrential equation with constant coeffecient
- 1. Presentation On Ordinary and Partial Differential Equations
- 2. Submitted to: Saba Fatema Submitted by: MD. Jahid Hasan ID: 152-15-5588 Sec: ‘E’
- 3. Solve the following second order linear differential equation with constant coefficient: 4 𝑑 2 𝑦 𝑑𝑥 2 -2 𝑑𝑦 𝑑𝑥 + 5𝑦 = 0 Soln : 4 𝑑2 𝑦 𝑑𝑥2 -2 𝑑𝑦 𝑑𝑥 + 5𝑦 = 0 …………….(1) Let, y= 𝒆 𝒎𝒙 be the solution of (1) The auxiliary equation is; 4 𝑚2 − 2𝑚 + 5 = 0 m= 2± 4−4.4.5 2.4 2± 4−80 8 2± −76 8 1/4 ± i 76 8
- 4. The general solution is; Y= 𝑒1/4𝑥[𝐴 𝑐𝑜𝑠 76 8 x + B 𝑠𝑖𝑛 76 8 x (Ans.)
- 5. THANK YOU