3. Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dBt 5 t y(1) = 2

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Q: Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dB %3D 5 t y(1) = 2

A: Given: dy=3-y5-tdt+dBt y1=2 We have to apply Euler-Maruyama method as one step to solve the SDE.

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Q: Use Runge-Kutta method of order four with step-size h = 0.5 to approximate the solution for 2<t<3 of…

A: given IVP isdydt=-y+ty1/2y(2)=2h=0.5here dydt=f(t,y)where f(t,y)=-y+ty1/2t0=2y0=2h=0.5by using R.K…

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A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

Q: y' + 3y = 5e2x – 6; y(0) = 2

A: since you have posted multiple question in this question which are not interlinked so i have solved…

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Q: 11. Solve the initial-value problem dx = -2x – 2y dt dy -2x + y. dt where the initial condition (x…

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Q: 2. Solve the initial value-problem: . dY dt Y with Y(0) = (1,0). - 4

A: The solution is given as

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Q: Find the general solution of dy 3 -my – ny | dt

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Q: 10. Solve the initial value problem dy dy +8 -9y 0 y(1) = 1, y'(1) = 0. %3D dt2 dt

A: We have given initial value problem, d2ydt2 + 8dydt - 9y =0 It's Auxiliary equation is given by, m2…

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Q: 6. Find the general solution to the DE. Show all of your work. dy =-0.2y+10 dt

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Q: Solve the initial-value problem dy :=-2y+u2(t)e~', y(0) = 3. dt

A: According to the given information, it is required to solve the initial value problem.

Q: 5) Given the system of differential equations 2 dx dy +2x-y=3t dt dt dx dy + +x+y=1 dt dt with the…

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Q: Solve the Initial Value Problem. (1 – 3t)– dy - у %3D 0, у(2) %3D —4 dt

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A: I have Transferred into a matrix differential equation and then solved

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Q: dt 4. Solve the initial-value problem dx = -2x – 2y dt dy = -2x + y, dt where the initial condition…

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Q: Q2: Consider the initial value problem. d²y dy y(0) = 2, dy (0) 3 a 2 0. + 2 + 6y = 0 dt2 dt

A: Since it is an homogeneous equation so complementary function is the solution

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Q: What is the general solution to the follwoing equation: (4t+5y+4)dt-dy=0

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Q: 6. Solve the second order linear IVP d²y Y at? dy 2 = 1. "6)-1 dt (dt Hint: dt- dy substitute dy…

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Q: Solve the initial-value problem. +3dy + 3t²y = 8 cos(t), y(t) = 0 dt

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Q: 2. Solve the initial value problem, if it is exact: (4y+2t – 5)dt+(6y+4t–1)dy = 0, y(-1) = 2.

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Q: Solve the given initial-value problem dr At = 3x + y – e", r(0) = 3, dt %3D dy 2x + 4y, y(0) = -4.…

A: Step:-1 Given system of differential equation is dxdt=3x+y-e4t,   x(0)=3dydt=2x+4y,   y(0)=-4 Take…

Q: 8. Find the solution y(t) of th d³y dy - 2y% = dt dt3

A: