Original subtitles

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Everyone just wanted you a couple examples of determining whether a differential equation is linear

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and why or it's not.

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And finding the order.

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So first of all the order is the order of the highest derivative.

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So in this case the biggest derivative is the second derivative it's the order of the highest derivative.

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So the order is to.

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In this case the order of the highest derivative would be three.

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And in this case the city why X to the fifth power.

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So the order of the highest rated is 1.

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OK.

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As far as linear and non-linear in Y.

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So a differential equation is linear in Y.

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If Y and all of its derivatives are to the first tower.

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So again y and all of its derivatives which are the first power and in front of Y in all of its derivatives.

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You only have pure functions of x.

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Ok so here y and all of these derivatives are to the first power and confront a Y.

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And all this derivatives you have pure functions of x all and you should have a pure function of actual

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here to.

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No problem.

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Right so this would be with you

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in this case.

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Same thing y and all its derivatives are to be first power but it would fail in front of Y in all this

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derivatives we have to have pure functions of x right.

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You have this little piece here.

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This makes it nonlinear.

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Right.

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We're not allowed to have that right.

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That's no good right.

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That's not a pure function of x.

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The function of y in front of the first derivative that destroys linearity.

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This example here.

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Why not.

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And then all of its derivatives have to appear to the first power fails right away.

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You have the first remitted to the fourth power.

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So this would be so again.

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And it will be linear in Y.

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Gentlemen speaking if y and all of its drivers are to the first power and you only have pure functions

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of x in front of y and all of its derivatives that's it.