Use Euler's method with step size 1 to estimate (¹), where y() is the solution of the problem y + 3x²y = x² with initial y(0) = 3 values

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: Use undetermined coefficients to find the particular solution to y'' – 3y' + y = 4t2 + 6t + 5

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Q: Use Euler's method and 4 steps to approximate y(1)

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Q: 3y = /2y – 1, y(1) = 1. ) Find the solution y = y(x) of this IVP. Please present your solution y =…

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Q: (x)= e°2× (x-1) us

A: Here The second method gives the correct result for an initial guess of less than one.

Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

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Q: ,(x) = (x-x+1) y'(x)+3y'(x)+9 y(x) = 5x' +1 true false

A: False

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: 6z dy (78)a

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Q: if x(t) = tsin(3t) is a particular solution to the equation x" + qx = cost3t, then q = -9. Is that…

A: The given differential equation is: x''+qx= cos t (3t) From the hypothesis, x(t)=t sin (3t) is the…

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: Problem 3 Solve the IVP y' = y(x3 + 1)' y(0) = –1. Please present your solution y = y(x) explicitly.…

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Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: se Newton-Raphson Method to find the approximate solution of the nonlinear equation f(x) giv en as…

A: To approximate the solution of the below equation using the Newton-Raphson Method. x3−x−1=0

Q: Find the general solution y = y(x) to the equation x > 0 and y > 0).

A: Use Bernoulli equation to solve

Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

A: Given, fx=30x4-121x3+60x2+64x With initial point, x0=4 Differentiating the given equation up to…

Q: Solve the equation 2 x " y " + 3 x y = (1 + x ) y = ху - which has a regular singula Point x = 0.…

A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

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Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

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Q: (x³-4x+1)vx++5x+5 find y' 4x2+5x

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Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

A: Given:-           The differential equation  is:…

Q: Find a third degree polynomial which approximates the solution to the initial va problemy" + 2xy -xy…

A: The given differential equationLets solve it using the Taylors polynomial

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