The difference between linear and non linear differential equation

fabianz
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I'm just starting to learn about ordinary differential equation and I'm still
don't know how to find the difference between linear and non linear differential equation.
I'm really confused about it, even after I'm reading my textbook:confused:.
Would someone help me please?
thank you very much:smile:
 
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its pretty much the difference between ones you can solve and ones you cannot.
 
Oh, now that's just silly! (Though pretty much true!)

fabianz, do you know the difference between linear and nonlinear functions?

A linear function must be of theform f(x)= ax+ b. Nothing more complicated than multiplying by a number and adding a number. For a function of several variables, "a" and "b" can be any function of the other variables and still be "linear in x". Any thing other than that is "non-linear".

A differential equation if "linear" if it does not involve any non-linear functions of the dependent variable
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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