2,d'y(0) = -2 dt? d'y(t) , dy(t) dy0) - + 3 dt = sec(t), y(0) = 2, dt %3D %3D dt

Q: Show that the 2-D Heat Equation dx² ди becomes ди if x = es cos w and y = es sin w. You ma dt dy?…

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Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

Q: d²y dy 4+ 5y = t dt dt2 dy y(0) = 0 (0) = 1 dt

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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: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

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

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Q: A mass-spring system is modelled by the differential equation u" + 16 u = 0 , and the motion starts…

A: Given that u''+16u=0   with   u0=7   and  u'0=4. Its auxiliary equation is m2+16=0. Solve as…

Q: If  x2 +y2+z2  = 9,dx/dt  =5 , and dy/dt  =4, find dz/dtwhen (x,y,z) =(2, 2,1).

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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: A mass-spring system is modelled by the differential equation u' + 16 u = 0, and the motion starts…

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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: Solve differential equation using Laplace transforms. d²y dy + 4 + 4y = 60 y(0) = y' (0)= 0 dt? dt

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?

A: Given:

Q: 4.Solve the pair of simultaneous equations dx =xy-t, x(0)=1 dt dy = x+t, y(0) = 0 dt From t=0 to…

A: You don't mention any method by which we can solve, so i use simple Iteration method Euler's Method

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

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Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

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

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Q: y? what is dt/dy? 2y +1 if t =

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Q: Find the differential dy. 1- 5x y = 4 dy = dx

A: Given that y = (1 - 5x)/4 Find derivative of this y. Here i attached solution of this question.

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

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Q: Calculate dy/dt using the given information. xy2=4; dx/dt=-5, x=4, y=1

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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: 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: if xy+x=12 and dx/dt=-3, then what is dy/dt when x=2 and y=5?

A: Given :xy +x = 12

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: y = tan (5t - 21 +1)

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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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: Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use…

A: Given dydx=x(y-8)2-6 We know that slope of linear equation id the it's derivative So, m=dydx

Q: ]If x' +y +z =9, dx/dt 5, and dy/dt 4, find dz/dt when (x, y,z)=(2,2,1).

A: Topic- application of derivatives

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: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

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Q: = 4x - 2y + 2U(t – 1) dt dy 3x - y + U(t – 1) dt x(0) = 0, y(0) ])•(C ])•(_ x(t) = | ) «(-[ y(t) :

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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: 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: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

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Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: 3. dy/dt = e e- -∞ <yo <

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Q: d²y 5 dy +6y= e7t dt dt2 y (0)=0 y'(0)=2

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Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: If x2 + y2 = 100 and dy/dt = 8, find dx/dt when y = 6.

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Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: dy dy + 7 dt + 10y = e-t dt2

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Q: 4. (4y+ 21 - 5)dt +(6y+41 –1)dy = 0, y(-1)= 2 cs

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Q: dæ Let y = 3.75a + 4.75 and dt 0.2. dy dt Find when x = 3,

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