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True or False? Justify your answer with a proof or a counterexample.The differential equation $y^{\prime}=3 x^{2} y-\cos (x) y^{\prime \prime}$ is linear.

True

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

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this question. We are asking you this or the is linear or not, you already know how to shake. If the first order would be linear or not by looking for this stand up foam Right. But that only tells you up to this like first order derivative. What happened when we have on a two on tree or more? Well, that is. First of all, I would say that this is yes, it is linear. But why is that? I will show you the like gender role. Way to see it is linear or not. This may not be strictly from the mathematical definition, but it is the way to shake anyway. So for the to be linear, it needs to have no function or the narrative off degree greater than one for gas on the word degree. Here, do not confuse degree with under in all the e order Other is how many times a day function God do with TV. This is the other 12 and three and so on. But they can all be degree one give. They are just stand alone like this. This is order one degree one. This is other two degree one. When you have multiple of them, however you like square or Cuba or whatever, then the degree will be to tree like depending on the power we also do not want even if is off different order. It is times together like this because of a degree more than one as well. We also don't want product off these So as I said, the one eye Why times didn t o r secondary tee times time, first Daytona teeth These If you have these, it will not be linear. So we cannot have any of these. We can have, however high like Hi. No matter how high you want are there on the function we can also help Just stand alone from shell like this. So back to our question we will see that we have Why here and why Double pram and why prom? But they are all off degree one. There's nothing attached to them. That is why So that is why we can say it is linear. Thank you

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