Linearity of differential equation

bhanesh
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Friends I have one doubt

Below given equation is linear or non linear

1387027772743.jpg


:)
 
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It's non-linear, because of the cos x coefficient. Compare it to the ODE for a pendulum, which is non-linear, but can be linearized if small deflections are assumed.
 
bhanesh said:
Friends I have one doubt

Below given equation is linear or non linear

View attachment 64770

:)
Mathematically,the equation you wrote is considered a linear ordinary differential equation with non-constant coefficients. It is considered linear if the homogeneous part is linear with respect to the dependent variable (in this case y).
 
But what about -5 term
 
bhanesh said:
But what about -5 term
That's not included in the homogeneous part.
 
Linear, because all exponents of y aren't different of +1.
 
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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