dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

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Q: 3. Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dBt 5 t y(1) = 2

A: Given dy=3-y5-tdt+dBty1=2

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Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

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A: solution is given below..

Q: Find the general solution of

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Q: 8. Solve: dx dt =x-4; dy dt = = 4y+t²; t = 0; x = 1; y = −3

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Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

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Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

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Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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Q: Determine the order of the differential equation. (dy/dt)^2+7 dy/dt+9y=3t

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Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

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Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

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Q: Use the Euler method to solve d²y 0.5t + y = 0 dt2 where y (0) = 2 and y'(0) = 0. Solve from x = 0…

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Q: Ql: verify that the indicated pair of functions is a solution of the given system of differential…

A: Given equations are x=e-2t+3e6t and y=-e-2t+5e6t. Compute the derivative with respect to t.…

Q: 6. Find the general solution to the DE. Show all of your work. dy =-0.2y+10 dt

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Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: d2y/dt2+5(dy/dt)+6y = t2+2t  Solve the equation using the method of change of parameters.

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Q: Solve the initial-value problem with the initial condition Y, = 0. dy = y + 3 dt %3D y = %3D

A: dydt=y+3 with the initial condition y0=0

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A: I have Transferred into a matrix differential equation and then solved

Q: dz 6te2z dt such that z(0) = 0. z =

A: see 2nd step

Q: (t -x)dt – tdx =0; when t = 1, x = 5

A:

Q: 2. Find the particular solution of (xy + x)dx = (x?y² + x² + y² + 1)dy satisfying the initial…

A: Using Variable Separable Method

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Q: 2. Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) =Q

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Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: H.W: Solve-Using D-operator dy dx + dt + 3y – 5x – e-t = 0 %3D dt dx dy + x + y - 3 = 0 dt dt 2.

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Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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Q: 4) Solve d²y + 4y = 2e¬t %3D dt2 Where y(0) = y(0) = 0 %D

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Q: 4. Show that al f(t) sin a(r – t)dt Y solves the initial value problem dy +a?y = f(x), dx? dy = 0…

A: The given initial value problem is                   d2ydx2+a2y=f(x), dydx=0 and y=0 when x=0. We…

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

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Q: 8. Find the solution y(t) of th d³y dy - 2y% = dt dt3

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.