43. y" – 16 y = 16 t²; y(0) = 0, y' (0) = 0; general solution y = cj e41 + c2 e¬41_R.

Q: a) Find the solution of this initial value problem and describe its behaviour for large t. The…

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Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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A: dydx= f(x , y)dydx=1x2(y+3)The Euler method is given by : yn+1=yn+hf(xn,yn)Here f(x,y) =…

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Q: Solve the initial value problem.   (ds/dt) = 8sin^2(t+(π/12))​, ​s(0)=5

A: In order to solve this we need to integrate it and then we can find constant by putting t=0

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Q: Solve the initial-value problem by using integrating factors. y' + y = x, y(0) = 6

A: Compare with linear differential equation and then solve

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Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: 4. Find a Particular Solution for the following differential equation [Apply the method that was…

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A: We use the definition

Q: Solve the Nou-linear differential equation casy Sinylla@şiny given that 4(0)=6

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A: The solution is given as

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A: For the solution of the problem follow the next steps.

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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A: Detailed solution is given below.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.