Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x = 0 to 1.0 using a step size of h=0.2 where y(0) = 2. show your results using a table. dy f'(x, y) = = -3y + 2e-* dx

Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

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Q: Find f'(z) of f(z) = 3πi.

A: Compare the given function f(z) = 3πi. with f(z)=u(x,y)+i v(x,y) So,  u(x,y) =0 and v(x,y) = 3π

Q: f(t)=−2t^2+t+1 Find the equation of the line tangent to the graph of f(t) at t=9 y=

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Q: Find the derivative of f(x) = e* (3x' - 4) %3D

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = −9t² + 21t + 8 L…

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Q: Differentiate the function. y = (3x* - x+ 1) (-x³ +9) %3D y' =] %3D

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Q: а. f(-3) %— 4 b. f'(0) = %3D 3 2 c. f'(3) = %3D d. f'(2) -5 –4 –3 -2 –1 1 2 3 4 5

A: To find: f'(-3), f'(0),f'(3),f'(2) Given information: The graph of f(x) is shown below.

Q: If a line intersects the x-axis at 'r' and the y-axis at '1/r', at what point (x,y) does it…

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Q: Find the GS of y" - y' - 12y = 0

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Q: Use implicit differentiation to find y' for 4x³y² + ln(xy³) Answer exactly. y' (1, 1) = 4 and then…

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Q: Find y' for (ry)”/” – 64 at the point (4,4). (wy)³/2 C At (4, 4), g' DE

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Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

A: Given: 25y''-70y'+53y=0  with the IVP y(5)=8 ,    and   y'(5)=1By…

Q: Find y as a function of x if x²y" – 3xy' + 4y = x", y(1) = 3, y'(1) = –5. y =

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Q: Find the | y' = 12x³ – 12x² – 12 Oy' = 6x² + 6x Oy' = 6x² - 6x Oy' = 12x + 6 derivative if y = 2x³ +…

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Q: Given f''(x) = 5x + 1 and f'( – 1) = - 5 and f( – 1) = 4. %3D Find f'(x) = and find f(2) Preview…

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Q: A function H is differentiable at x = 2. An equation for the line tangent to the graph of H at x = 2…

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Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: 2 Determine f'(x) given f(x) = (2x + 4)? • Vx. %3D

A: fx = 2x+42×xApply chain's rule ,f'x = ddx2x+42×x +2x+4ddxxf'x = 2×2x+4×d2xdx×x +2x+4×12xf'x =…

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.