Differential Equation Tutorial 1
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This tutorial document provides 4 partial differential equations and asks the reader to determine the order and linearity of each equation. It also asks the reader to find the values of m that satisfy two ordinary differential equations, where y is defined as a function of m. Specifically, it asks the reader to find the values of m such that y=xm and y=emx cos(nx) are solutions to two given ODEs.
Differential Equation Tutorial 1
- 1. TUTORIAL 1 1. Determine the order and linearity of the following DE. d3y d4y (a) = 1+ dx 3 dx 4 ∂3 t ∂2 u ∂4 t ∂u (b) + − + − sv = ut ∂s 3 ∂v 2 ∂v 4 ∂v d4y d2u (c) + + u = xy dx 4 dx 2 ∂2 u ∂3 w (d) 2 − 3 + w = y3u 2 ∂v ∂y 2. Find the values of m so that y = xm is a solution of d2y dy x2 2 - 3x - 5y = 0 dx dx 3. Find the values of m and n if y = emx cos nx is a solution of d2y 2dy 2 + 2y = dx dx