Find the general solution to dx = x + y – z dt dy 2y dt dz = y – z dt

Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: 8. Integrate by parts: a) St csc? t dt b) S x2 In x dx

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

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Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

Q: Given x= 2y? , evaluate dx dy at y = 1 and dt dt 3.

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Q: (a) x = 0: dy/dt (b) x = 2: dy/dt (c) z = 3: dy/dt

A: Given that x2+y2=25, and dxdt=6 we have to find dydt when y>0 and  a) x=0b) x=2c) x=3 Important…

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

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Q: If x^2+y^2=36 and dx/dt=9, find dy/dt when y is positive and (a) x=0: dy/dt= (b) x=2: dy/dt=  (c)…

A: Given: x2+y2=36    -1⇒y2=36-x2⇒y=36-x2   -2dxdt=9   -3

Q: dx? dy = y(t) - dt2 dt dz x(t) + dt dy dx z(t) = 0 dt dx + 3x(t) + 4y(t) + 3z(t) = 0 dt dt when x…

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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: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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

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Q: Find the solution to dy/dt = 6y Satisfying y(1)=7 y = ?

A: Firstly , separate the variables and then integrate and solve. ∫1ydy = ln(y) +C ∫tn dt =tn+1n+!+C

Q: Assume w = x2y4, where x and y are functions of t. Find dw>dt when x = 3, dx>dt = 2, dy>dt…

A: Given:  w = x2y4, x and y are functions of t  To Find: dw/dt when x = 3, dx/dt = 2, dy/dt = 4, y = 1

Q: Assume that x = x(t) and y = y = y(t). Let y=x^2+4 and dx/dt =2 when x=5. Find dy/dt when x=5

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Q: d²y Find the solution to the IVP dt2 dy + y = 0 where y(0) = – 2, dy (0) = 5. dt y(t) = Preview

A: Steps are follows . Auxiliary equation and solution of the equation . General solution . And values…

Q: Find the general solution of dt z(t) = Az where z = y(t and A =

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Q: (dx = x - y+z dt |dy = x +y – z dt dz — 2х — у dt

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

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Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

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Q: Given: y=fso(x-1) dt - dy =D{(x). dx show that

A: We will prove the following result using Leibnitz rule.

Q: 6. dy dx + y?x = sin y, dx ay = 7. dt dt 8. Σa (x) dx) d0y = f(x), where d°y = y, dx°

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Q: the = x + y + 3z dt dy a) = 2y + 3z dt dz = 3z %3D dt 1. Write the linear s Find the eige envalı

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Q: Using d²y(t) dy(t) + t dt + 2y(t) = 0, and y(0) = 0 and y' (0) = 1. t dt?

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Q: J(Fi+ーD j) dt b) Integrate:

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Q: Determine the Integrating factor of the DE: y (x³e*y y) dx + x (y + x³e*y) dy 3 1

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Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx+ x(x+2y)dy =0 2 A 2 © x²

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Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

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: 1. dy ==2(y+1);=3y-x+e³; t=0; x = 1;y=1 dt dx dt

A: SOLUTION: Given: dxdt=2(y+1)   ;  t=0;x=1;y=1dydt=3y-x+e-3t

Q: dx dy -2.x. (d) = Y, dt dt

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Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: The integrating factor of the linear DE dy + ycot x = sin x dr

A: Given: dydx+ycotx=sinx

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

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Q: What is an integrating factor of the DE dy/dx = (y + y^2) / x ?

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Q: Assume w = x²y*, where x and y are functions of t. Find dw/dt whenx = 3, dx/dt = 2, dy/dt = 4 and y…

A: To find the derivative of the given function w,  we need to apply chain rule of differentiation and…

Q: Find dy/dt if y is as follows. t2 + 4 y = In 7 - t dy dt II

A: We use logarithmic properties to simplify the given function and use chain rule to solve this…

Q: dx dt dy dt x(0) = 2 y(0) = 1 3x – Y 9х — Зу

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Q: Find dy/dt using the given values. y = x - 3x for x = 4, dx/dt = 4. dy dt

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Q: Find given that dt x² + y² = 2x+4y, x = 3 y = 1, and dy dt i dx dt

A: SOLUTION-

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: Find dz/dt dz/dt given:  z=xe2y, x=t6, y= -1+5t

A: Given,         z=xe2y    , x=t6     ,    y= -1+5tWe know that,            ∴dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: 12

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Q: Can you help me step by step?

A: The given function is

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

A: We have to solve the problem

Q: Please show all work

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Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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Q: If+y = 25 and dz/dt = 5 , find dy/dt when y is positive and %3D %3D (a) z = 0 dy/dt = 0 (b) z=1…

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