dx dy (a) dt di -y = 6e3t, 2 dt -3x +-3y = 6e3t; dt x(0) = 3, y(0) = 0.

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is…

A: From the figure, the critical points are 1, 3 and 5. Thus, f(y) should contain powers of (y-1),…

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t x(t) general solution function

A: Given equations are                                              dxdt+dydt+x=e-t           ...…

Q: determine the differential equation of the family of lines passing through the origin. x dy - y…

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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: d?x ax dx ÷+ 9x = 0, when x(0) = 1 and (0) = 0 dt2 dt dt

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Q: e-Using dy dx dt + Зу -5х —е t — dt dy +x+y- 3 = 0 dx dt dt

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Q: dx dy - 2x – 2y. a) dt -x, dt dx = x + 3y, dt dy dt 2.x. b) dx dy (c) 3x – 4y, 2x – y. - dt dt

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Q: dx 2х — dt dy – y = 6e3t, dt. dx 2 dt dy 3x + dt - 3y = 6e3t; %3D x(0) = 3, У (0) — 0. %3D

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 2) t (y-1) dt +y(t+1)dly=0 31 хчуу! -2y =. 41 yan- x lnn dy ==

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Q: * = x- 2y+ 2z = -2x+y– 2z dt dy dt E = 2x – 2y+ z dt

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Q: Solve IVP: dx x + Y, (0) = 0 dt dy 4x + Y, y (0) = 3. dt

A: Since you have posted multiple question we are supposed to give solution of first one only ...kindly…

Q: Find the solution to the initial value problems using integration. dH/dx=3x, H(0)=1…

A: Consider first problem:

Q: dx dy -- x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: We will find out the required solution

Q: dy - 2y = 0, x(0) = 4, y(0) = 0 dt dx --x - 2y = 16te', 2x – dt

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Q: y = tx2 + tx dy Find dx dy dx + 2tx * dy Find dt dy dt II

A: Given that y=tx2+t4x We have to find dydx  and dydt dydx is the derivative of y with respect to x…

Q: dx dy + y = x , dt = 3y dt dx dy 1.

A:

Q: dx -x+3у dt dy -3х + 5у dt

A: Given the differential equation is  dxdt=-x+3y......idydt=-3x+5y..........ii…

Q: dx dy - x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

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Q: The integrating factor of the differential equation x+y =x is dx a) x b) c) y d) y

A: We have to find integrating factor of given differential equation.

Q: dy_y + x² + y2 dx y(1) = 0. Show that the differential equation is homogeneous.

A: To show that differential equation is homogeneous

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: dx dy - x – 2y = 16te', 2x - dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: The given differential equations are                                  dxdt-x-2y=16tet ..............…

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

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Q: 1 y' = 1– sint - y(t)dt, y(0) = 0 0,

A: Given the equation y' = 1-sin(t) -∫01y(t)dt. Initially, we integrate both sides of this equation…

Q: The integrating factor of the non-exact differential equation (r*y + y°)dx – (3° + x*y)dy = 0. is 1…

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Q: d² y dy } +24% +y=sinh3t – 5 cosh3t ; y(0) = -2, dt² dt y (0) = 5

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Q: y (y^3-x) dx + x(y^3+x) dy=0_At· muon

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Q: 2. Find dy/dx a) y = dt, x> 0

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Q: An integrating factor of the differential equation y Y+ + 2²/²³ + ²/²2 ) dx + 1⁄2 ( x + xy²) dy = 0…

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Q: (y')² – 3yy' + xy = 0 12 +y = x \dx², S + (S + = 0 dt² dt² dy x*y" + xy" = ex ds t2 \dt², () - t=1 –…

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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: dx x + y + 1 dt dy x + y +1 dt

A: Given dxdt = x+y+1                          (1)dydt = x+y+1                          (2) Then dxdt =…

Q: Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

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Q: he given initial-value problem. dx = y - 1 dt %3D dy -6x + 2y dt x(0) = 0, y(0) = 0 0, у (0) %3D 0

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Q: The differential equation (-xysin x+2ycos xdx +2xcos x dy 0 is

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Q: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

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

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Q: Use separation of variables to find the solution to the differential dy equation 0.3(y - 300) if y =…

A: Variable separable differential equation

Q: dx = x- y + 1 dt dy = y - x + 2 dt

A: Given: dxdt=x-y+1                       1dydt=y-x+2                       2 The above system of…

Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

A:

Q: dt 4. Solve the initial-value problem dx = -2x – 2y dt dy = -2x + y, dt where the initial condition…

A: To find the solution of the given system of differential equations.

Q: Show that: (xy? ) is an integrating factor of the differential equation dx dy хуз у4 r.IV 2y dx + 3x…

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Q: Solve simultaneous equation dx/dt=2x+3y , dy/dt=x+4y , x=-3 , y=1

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Q: dx 2x - y dt dy

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Q: The general solution for the flowing differential cquation is * (3x+ycosx) dx +(sinx-4y )dy =0

A: We will split the equation into separate differential forms and then integrate accordingly to get…

Q: Determine the differential equation whose integrating factor is x2 A (2у-3x) dx + х dy%3D0 B В y dx…

A: Suppose we have the first order differential equation dydx+Py=Q,where P and Q are…

Q: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

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Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

A: