1.8 - Solve the following ordinary differential equations, and specify how many and what kind of boundary conditions are needed. Identify dependent and independent variables. d а) dr `r dr (1d(rc), = 0 b) у - 2у -8у %3 хе* +4 2х с) у 1+x? V =1 1.9 - Solve the following O.D.E y +4y +5y = 8 а) y(0) = 2, y'(0) =-5 b) x²y" +xy' +9x²y=0 (Find the general solution) 1.10 - Show the solution to the following differential equation: d²y x dy dx? = 0 2 dx y(0) = 1, y(0) = 0 is y = erfc) 2 where erfc(x) e do

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.