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

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

A: The solution is given as

Q: Find an integrating factor for the DE y(4x – 3y – 3)dx +x(x– 2y –- 1) dy=0

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Q: dx + dx dy e; dy = x +y Use elimination to solve: dt dt dt dt

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Q: dy dx ; x = 0, y = 1 , t= 0 dt dt 2) x = t2 + t y = t2 -t -00 <t < 00 %3D fall

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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: Solve simultaneous equation dx/dt=x+y , dy/dt=4x+y , t=0 , x=2 , y=5

A: First I have written the differential equation into operator form and then reduce it into linear…

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

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

Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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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: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: QI Find d for dt dy = 4e - 5x'e0 dx dy 3x e +5x'e dx الخبار ه 2 dy dy 2xe 2e + 4xe* dx dx dy 5x'ere…

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Q: dy = 3. dt dz at (x, y) = (3, 1) and z² = x² + y² if dx = 1 and dt Find dz Preview dt

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Q: y = 2 (x² – 3x) (a) Find dy/dt when x = 2, given that dx/dt dy/dt = (b) Find dx/dt when x = 7, given…

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

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Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

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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: dy 3x2 + 2 and dt dx Find 3 if y = – 2. at x - dt dx dt

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Q: Find the integrating factor a. (xy+y2)dx+(x2+3xy)dy=0   b. (y2e2x+1)dx+(2ye2x-ex)dy=0

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Q: y = 2 (x² – 3x) (a) Find dy/dt when x = 2, given that dx/dt = 4. dy/dt = (b) Find dx/dt when x = 9,…

A: First we will derivative with respect to t then find both value

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

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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: 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: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

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

A: The objective is to find the general solution of system of differential equations…

Q: dx 3x – 5y dx = 3x – y + 2z +t-1 dt dt (a) dy = 4x + 8y dt dy (b) 2x -z- 3t2 dt dz x+y+z+t? dt

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Q: dx 5 x + 2y 2 dt dy 3 ーX 4 – 2y dt

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Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: Solve for the integrating factor * y (x + y) dx + (x + 2y – 1) dy = 0

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Q: dx 3x 6y = 0 dt dy 3x + Зу %3D 0 dt

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Q: Find the integrating factor: x^2 dy+(2x^3 y-e^x )dx=0

A: First order linear differential equation of the form dydx+P(x)y=Q(x) Integrating Factor:…

Q: Solve y(1): dy/dt + x = 1; dx/dt-y + 4e¹ = 0; x(0)=0 and y(0)=0.

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Q: dy + 2.xy= 5x² is dx The integrating factor of

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

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Q: (2) An integrating factor of (xy³ + y)dx + 2(x²y² + x +y*)dy = 0 is (a) y (b () (d) 2xy

A: We need to find an integrating factor of xy3+ydx+2x2y2+x+y4dy=0 Now, a differential equation of the…

Q: dx = 5x + y; dt x(0) = 2 dy -3x + y; y(0) = 0 dt

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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: Find the integrating factor of y(2x - y + 1)dx + x(3x – 4y + 3)dy = 0 Oy? 2x О ху Oy

A: See the details solution in below

Q: dx dt dy dt x + 2y -2x – 3y x(0) = 1 y(0) = 2 | |||

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

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Q: dx (b) (t– 2) – x = (t – 2)' , x(4)=10 dt dx (c) +5x -t = e" , x(0)= dt

A: Here we have to solve given initial value problem b and c.

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

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Q: Find the integrating factor. a. (xy + y2)dx + (x + 2y- 1)dy = 0

A: We have to solve the problem

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

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

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Q: Find dx dy dy and dt' dt dx x = 9t – 9ln(t), y = 4t2 – 4t-2 dx dt dy dt dy dx

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