1-a) Use Runge Kutta fourth order method to integrate y'= 4e0.8² -0.5y from t=0 to 3.0 S with step size of 1. The initial condition at t=0 is y=2. Note that the exact solution can be determined analytically as Q. Sr -e-05²) +2e-0.5t 4 y==(e° 1.3

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with a step size of 2. Solve exactly…

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Q: Find the general solution af the equation, y' = x(1- y).

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Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

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Q: Determine (without solving the problem) an interval in which the solution of (9-1²)y + 2ty = 4t²,…

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Q: x² + y² Use Improved Euler's Method to approximate y(2) for y' = Use h=0.2. Calculate up to 4…

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Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: Find the solution of with y(0) = 7 and y'(0) = 6. y" + y − 2y = 54 et

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Q: Use Euler's method with specified step size to determine the solution to the given IVP at the…

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Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: Solve the following Bernoulli equation y' – y = (2t – 3)y i

A: Bernoulli Equation : Consider y'+p(x) y=q(x)ynThen we let v=y1-nAnd solve the equation by…

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Find the general solution of the following equation valid near the origin: (1+4x2)y''-8y=0

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Q: Use Euler's method to approximate the solution to y' = 2ty – 2 , y(-1) = 2 on the interval [-1, 1]…

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Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…

Q: Solve the given problem: y'' + 4y= 3sin2x

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Q: Use the method of successive approximations to solve the I.V.P y' = y(1– 2x), y(0) =1.

A: Given The given I.V.P is y'=y1-2x,         y0=1. Apply Picard's formula or successive approximation…

Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with step sizes of 1. Solve exactly and…

A: Given that, h=1t0=0y0=0ft,y=3t

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0

A: According to the given data, find the general solution:

Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

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