. Consider the initial-value problem y'= 0.1!y+0.4x², y(2) =4. Use Euler's method to obtain the approximation of y(2.5) using h=0.1 and then h=0.05.

Q: Use h = 0.1 and Heun’s method to find solution to y'' + 3y' = 12 with y(0) = 5, and y'(0) = 1.…

A: Given: Use h = 0.1 and Heun’s method to find solution to y'' + 3y' = 12 with y(0) = 5, and y'(0) =…

Q: = - 6.24. Take an equation y' = (y − 2x)g(x, y) + 2 for some function g(x, y) such that g and 29…

A: Step 1: Step 2: Step 3: Step 4:

Q: 4. Solve the particular solution of y" + 3y' + 2y = 6e¬, y(0) = 1, y'(0) = 2, using a. Variation of…

A: we have given the differential equation y"+3y'+2y=6e-ty(0) = 1, y'(0) =2 we have to find the…

Q: 3-2r . Find y'(0) %3D

A: Given: y=3-2x21+x To Find: y'0=?

Q: y" – 2y + y = 1+x?

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Q: (8) y'= 4x +x? -y, with y(0) = 4, h = 0.05, find to 3-decimal.

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Q: Given the initial condition y(0) : e–2y = y'? 3, what is the particular solution of the equation…

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Q: Use Euler method to approximate the value of y(0.1), given y' - x2 - y = 5, y(0) = 3 with Ax = 0.025…

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Q: Find a general solution to y" +3y"-y'-3y=0.

A: Here we have to find a general solution to  y'''+3y''-y'-3y=0

Q: 3. 3. Using Euler's numerical method, solve the following. From x= 0 to 1.4 using a step-size (h) =…

A: Given dydt=x-y, dxdt=x+2y and h=0.25, y0=2, x0=1

Q: 5. (y – x + 3)dx + (x + y + 3)dy = 0; x = 1; y = 4. Solve in two different methods.

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Q: 2. Solve IVP y" – 4y' + 4y = 0; y(1) = 1, y'(1) = 1 Cind a general solution

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Q: Find the general solution to y" – xy' = 0. -

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Q: no. 3

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Q: (a) (2e – x)y' = 1.

A:

Q: 6. Solve the initial value problem: dx (x² + 2y²). = xy, y(-1) = 1 dy %3|

A: First of all write the given initial value problem in MDX+Ndy=0 form which is the homogeneous…

Q: 5. Solve y'=x +y given y(1) = 0. Find y(1.1) and y(1.2) by Taylor's meth- od.

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Q: 21. y' - 2y = f(x), y(0) = 1, where 1-x, 0, f(x) = if x < 1, if x ≥ 1.

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Q: 4. Find the explicit result for function y (i.e. function y = an function in term of x) of the…

A: (4) Given differential equation is  dydx=3xy+x2y                         y0=-4 It can be written as…

Q: 3. Approximate value of the root of the given equation f(x) = – 3x + 5x + 14x between 2 and 3 within…

A: The given problem is to find the approximate root using secant method in between 2 and 3 with Ea=0.…

Q: Q4. Solve numerically by using Runge-Kutta method y' =√xy+1 with y(0) = 1 to find y(0.05 and h =…

A: 4. Given,                  y'=xy+1;    y(0)=1.  To find the value of y(0.05) and h=0.025.

Q: Find the solution of y′′−6y′+9y=200e^8t with y(0)=2yand y′(0)=8.y=

A: For the given differential equation the complementary function can be determined by the method of…

Q: Find y' if xy = yx. y' =

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Q: 4. Solve for Y (s) given ty" + y' + ty = 0 y(0) = 0 %3D

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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: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

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)=?…