Intro to Differential Equations Solve the differential equat

Intro to Differential Equations

Solve the differential equation seen in the picture below.
Please show work so it is easy to understand. Thanks!

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Solution

Ans-

The general solution of the second order DE

y\'\' 3y\' + 2y = 0

is

y = Ae^2x + Be^x

If we have the following boundary conditions:

y(0) = 4, y\'(0) = 5

then the particular solution is given by:

y = e^2x + 3e^x

Now we do some examples using second order DEs where we are given a final answer and we need to check if it is the correct solution.