For what value(s) of the constant a is the differential equation d^2x/dt^2 + (a^2 - 3a)x dx/dt =...

Question:

For what value(s) of the constant {eq}a {/eq} is the differential equaiton

{eq}\displaystyle \frac{d^2x}{dt^2} + (a^2 - 3a)x\frac{dx}{dt} = te^{(a-3)x} {/eq}

a linear equation?

Linear Differential Equation:

A Differential Equation is said to be linear if it contains only terms that are linear in the dependent variable or its derivatives. Also the dependent variable and their derivatives should not occur in the multiple operation.

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What is a Linear Equation?

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Chapter 1 / Lesson 3
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Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.


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