4. Modify the Euler method to obtain the approximate values of y(3) and y'(3) y" – y' + y = t, 2

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Q: 1. 2. rning Find first derivative and second derivative of dependent variable a.y=x²+x+8 b. y=-x²+3…

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A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: 5. Use the method of variation of parameters to find the general solution to _y"—y'—2y=e³x.

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Q: Let A = (²2²) 22 Find et and the general solution to X' = AX + (1)

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Q: Find y'' for y = 4+ 5X 3

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Q: find y(x) for x2y'-2xy=3x with y(1)=3

A: Given,         x2y'-2xy=3x  with y(1)=3

Q: suppose that alpha(t) = 12t^2-6,with v(0) = 5 and s(0) = 10 find s(t) and graph alpha(t), v(t) and…

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Q: Let y' = y(y-3) Use Euler's method to approximate y(1) for the function y satisfying y'=y(y-3) and…

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Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: Q1. Find the general solution for the non-homogen 1st OLDE using undetermined coefficient method.…

A: Given Y'=-3-456Y+5-6ex

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: Find y' if ey+y²=2x. yey – 2 y'= хе + 2у хе + 2у y'= ye – 2 хе*У + 2у y'= 2 – yey 2 – ye y'= хе*У +…

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Q: Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties when…

A: We need to Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties…

Q: 3) Consider the IVP y' = x − 2y, y(0) = 1/2. Determine which of the two curves shown in the figure…

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Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: From Variation of parameters for the 2 -1 X' X + e 3 -2

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Q: Determine 4sin(x); the value of the arbitrary constants y(x) = C₁e* + c₂e¯* + y(0) = 1, y'(0) = -1…

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Q: Let 2² + y? = 1 and y(0) = 1 Then y'(0)= none of the listed here 1 -1

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Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: Given G(x, y) = 6y²(e(²) +e (¹)), where and y are found to be In 3 and 3 with maximum possible…

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Q: 1) Show that (a) y =xe satisfies the eq. xy' (1-x)y (b) y =xe"A satisfies the eq. xy'=(1-x²)y

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Q: (1+x2) y' + 2xy - 4x2y3 = 0 (Bernoulli)

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Q: See attached

A: Given function,

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

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Q: 8. use "Linear equation" method (x*y+x'cosx)dx-x'dy 0

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Q: 1. Find y'. (a) v5æy + 2y = y² + xy³

A: Differentiate wrt x