General Solution for dy/dt=2ty+4e^(t^2)

stasianlov
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find general solution for differential equation dy/dt=2ty+4e^(t^2)

i got e^(t^2)(4t+k) is that right?
 
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hi stasianlov! :smile:

(try using the X2 button just above the Reply box :wink:)
stasianlov said:
find general solution for differential equation dy/dt=2ty+4e^(t^2)

i got e^(t^2)(4t+k) is that right?

yes that's fine :smile:

what is worrying you about that? :confused:​
 
you can check the answer by substituting the solution y(t) and its derivative dy/dt in the differential equation. The results should be 0.
 
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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