DE

What does linearity mean in differential equations?

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See here. Second section.

You really could so easily have Google'd that.

My textbook says dy/dx = x^3 + y^3 is linear?
How so?

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My textbook says dy/dx = x^3 + y^3 is linear?
How so?

Thanks!

What does linearity mean in differential equations?

Thanks!

It means that the dependent variable and all its derivatives are multiplied by constants only, not by themselves nor by functions containing the independent variable..

For example, (dy/dx) + xy = 0 is non-linear

but (dy/dx) + y = (x^2)coswx is linear.

(Note that it doesnt matter how the function of the independent variable is)

If (dy/dx) + xy = 0 is non-linear why is no. 1 on the picture linear?

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If (dy/dx) + xy = 0 is non-linear why is no. 1 on the picture linear?

Thanks!

It means that the dependent variable and all its derivatives are multiplied by constants only, not by themselves nor by functions containing the independent variable..

I suspect you're confusing two concepts; a linear ODE, and a linear ODE with constant coefficients (see quote).

$\frac{dy}{dx}+x^2y=x$

is a linear ODE, but it does not have constant coefficients.

Linearity basically tells you that if y = u(x) is a solution to the DE and y = v(x) is another solution, then y = au + bv will also be a solution, where a and b are constants.

If you google Linear Differential Equation you'll find there's a decent Wikipedia article on it!

Hi, i just wanted to ask.
Would i be correct is saying that ydy/dx = 3 is non linear differential equation?
Because then the dy/dx and y would not be linear?

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Thanks for the reply in the other post btw!
SO in no.1 in the picture, is it linear?
And why?

Thanks!