9. Given: 2-2 + 2y = e²t Sint, 0 < t < 1, y(0) = -0.4 and y'(0) = -0.6, dt Find by Runge-Kutta Fourth Order Method: (e) y(0.1) (1) d (0.1) dt Use a step size of h = 0.1

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

A:

Q: b) Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80 cm long…

A: b) Given :-  The temperature ux,t from the heat equation in a laterally insulated copper bar 80 cm…

Q: Solve dy dx =-y with y(0) = 1. Find y(0-01), y(0-02) by Runge-Kutta method.

A:

Q: Convert y " (f) + (1 – t) y' (t) + e¯' y (t) = t – 5t; y (0) =- 3; y' (0) = 4 into an in tegral…

A:

Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

A:

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

A:

Q: x² + y² Use Improved Euler's Method to approximate y(2) for y'=- xy ; y(1) = 3 Use h=0.2. Calculate…

A: Given:The differential equation is given as with and .To find: using the improved Euler…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Let D: PS(R) → P3 (R), be where D(f) = f'. calculates Ker(D)…

A:

Q: Use RK2 (Heun's method) with h = 1/4 to estimate y(4/4) given Yo 30: Y1- Y2: Y3- Y4: 3/13 3/2: Y'3:…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value. y' =…

A: To solve the given differential equation by Runge kutta Method of order 4 first we fill find the…

Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.2) using the…

A:

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

A:

Q: where and dt=2' y(0) = 1, y(0.1) = 1.01, y(0.2) = 1.022 (03)

A:

Q: Given the initial conditions y(1)=1 and y'(1)=0, estimate y at x=1.2 using a stepsize h=0.1. Use…

A:

Q: Solve (t² + 4) da = (x² + 16), using separation of variables, given the inital condition x(0) = 4. x…

A: To solve the following initial value problem by using separation of variables.

Q: LET F(X) =2 x SIN(X), = 2 x 10" TIMUM STEP VALUE THAI CAN BE USED WIIH CENTRAL- DIFFERENCE FORMULA…

A: We know that the optimal step formula for the given value of epsilon and the upper bound M is given…

Q: Use Euler method to approximate the value of y(0.1), given               y' - 4y = 3x2 ,  y(0) = 4…

A:

Q: 1. Solve for y: (a) x² + y = 20 (b) 3y - t = t³-y (c) xy + zx = y (d) 2ye - e In x = 3x4

A:

Q: Solve y(t) – [ (1+u)y(t – u)du = 1~ sinh t

A: Consider the given:…

Q: min13л1 + 4x1р + 1; — Зл1 + 2т, x'0) = (0.5,0) What is the step size for the first step? use armijo…

A:

Q: Let y be the solution of the equation y' = 4 - 2xy satisfying the condition y (0) Use Euler's method…

A:

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

A:

Q: z = xy dy x2+y= 2x/1-x’y² dx 2. Using the substitution ,change the to a separable equation. Hence…

A: We are given the differential equation  xdydx+y=2x1-x2y2 we have to use the substitution z=xy.

Q: cos(x) * еУ + 9у %3D Зу8 — 5х + 10е =

A: The expression cos(x)×ey+9y=3y8-5x+10e. We have to find y' or dydx.

Q: [23] R and f 5 sec(t) 0

A:

Q: find the general solution of y''+y=cos(t) using the variation of parameters method

A:

Q: Approximate y'(1.6) in the function y'= 5x-2y when y(0) = 1.5, x(0) = 0.4 and the stepsize is 0.2…

A:

Q: (x² + 1) d x + 3x(y - 1) = 0, y(0) = 7 + 1) ( ² 2 y = 1 + 6(x² +1)

A: The given differential equation is; (x2+1)dy/dx +3x(y-1) =0, y(0)=7.

Q: 8. (y – In æ) dæ + (x +1) dy = 0, y(1) = 10 Ghenoral Form : y' + Pixly= Q(x) I (x): PLk) du : Final…

A:

Q: x' = 10 t² x², x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately calculated…

A: Given differential equation is, x'=10t2x2, x0=3.

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

A:

Q: Ex.1. Use Euler's method to determine an approximate x=0.2 from the IVP dy = = 1 -x + 4y, y (0) = 1…

A:

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.