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ddd [48]
3 years ago
15

What is the sum of the given polynomials in standard from? (x^2 -3x) + (-2x^2+5x-3)

Mathematics
1 answer:
galben [10]3 years ago
8 0

The pic will help you

Good luck:))

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Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist
charle [14.2K]

Answer: t = - 5 ∈ I_{1} = ( -∞ , -4 )

Step-by-step explanation:

The standard form of O.D.E is written as :

y^{1} + p(t) = g(t)

Equation given :

(16-t^{2} )y^{1} + 9ty = 5t^{2} ,       y(-5) = 1

The first thing to do is to write the O.D.E in standard form , that is we will divide through by 16 - t^{2} , so we have

y^{1} + \frac{9ty}{16-t^{2}}=\frac{5t^{2}}{16-t^{2}}

With this , we can see that p(t) and g(t) are both continuous in the same domain. Therefore , the intervals are :

I_{1} = ( -∞ , -4 )

I_{2} = ( - 4 , 4 )

I_{3} = ( 4 , -∞ )

recall that y(−5) = 1 , then t = -5

This means that :

t = - 5 ∈ I_{1} = ( -∞ , -4 )

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