Find an approximation for the solution of Y"(t) + 4Y"(t) + 5Y'(t) + 2Y (t) = 2t² + 10t + 8, Y (0) = 1, Y'(0) = -1, Y"(0) = 3. at t=0.2, by employing Euler's method with the step size h=0.1.

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Q: Find the solution to y '= 3y satisfying y(2) = 1000.

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Q: Find a general solution to the given equation for t<0. (t^2)y''(t)-5ty'(t)+15y(t)=0

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: y" (t) + 2y' + y(t) = 8t²e-t.

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Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Find y(3) for y' = 1 + (x-y)2, y(2) = 1 by using Improved Euller's method. h = 0.5

A: Given  y'=1+x-y2 y2=1, h=0.5 We will find the value of y3

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: Find the solution of y"-y'-6y = -e* +12x with y(0)=1, y'(0)=-2 by method of undetermined…

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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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: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Q2) Solve: y" - 5y' +6y=H(t-1), y(0) = 0, y'(0) = 1.

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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Q: y' = (1-x²)y , y(1) = 1, h = 0.1 1.0921 1.0986 1.0974 O 1.0935

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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: (B) Find the general solution of x'y" + xy' -y=x²+1 given that y, = x is a solution of the…

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Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

A: We take y'=z the Given equation is y''=y+xz,y(0)=1,y'(0)=0,y(0.2)=?…

Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: Use the backward Euler method with h = 0.1 y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5   find y(2)

A: Given y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5and h = 0.1

Q: Solve 2y-y² sec²(xy²) + (2x−2xysec² (xy²)) y'= 0; y(1) = 2

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Q: Solve []-[*一- -15 a'(t) y'(t) z'(t) 1009 1000 x(t) y(t) z(t) 500 2 500 400 12 1000 400 with…

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Q: Use the Runge-Kutta method to solve the equation y" = xy' +y for x= 0-0(0-2)2-0 given that at x = 0,…

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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.