Is (1+y^2) d^2y/dt^2 + t dy/dt + y = et a Linear Equation?

patrickbotros
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(1+y2) d2y/(dt2) + t dy/dt +y = et
 
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I think its not linear, there's y squared
 
No, it's not.
 
It is not because, as Leonita said, it has a non-linear function of the dependent variable, y.
 
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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