d²y + 3 dy dt dt +2y = 5(t−5)+U(t−10), y(0)=0, y'(0)= — -

Q: dt = (c) (9+t2)3/2

A: Given:

Q: general equation of (z-t)dz=(z+t)dt

A:

Q: et y = f(x) = 5x² + 3x + 5 and x = g(t) = 2t + 3. Find dy = dy dt

A: Given query is to find the derivative.

Q: Use matrix exponential to find the solution of dx dt 16 5 3 Y, 9. Y, dt x(0) = 1, y(0) = 1

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Q: find the a general solution to dy/dt = {{-9,12},{6,-8}}y

A: (.)  Given ,            (.)  Consider a system of differential equation ,…

Q: Solve for an autonomous equation? dy/dt = f(y)

A: An autonomous first-order ordinary differential equation is an equation of the form

Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

Q: d²y dy +2 + 2y = e-t dt² dt y(0) = 0, y'(0) = 0

A: d2ydt2+2dydt+2y=e-t y0=0y'0=0

Q: 4) Equation: 4x +9y² = 1 1 Given that dy/ dt =8, find dx / dt when (x,y)= 3 9

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Q: at (x, y) = (1, 2) and z² = x² + y² if. dt = 9 and dy dt = 2.

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Q: e"dt=

A:

Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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Q: dx x(0) = 1 у (0) — — 2 х — 2у %3D dy dt 4x 3y %3D ||||

A: I have followed the steps which are given in the problem

Q: ds/dt if s=(t9+6)(t8-6)

A:

Q: Let F(x) = Vt2 + 19 dt. Find 6. (a) F(9) = (b) F'(9) =| (c) F"(9)

A: Topic = Derivative

Q: d³y + y = 4t Sin(t) , y(0) = 0 = y'(0)

A: We are given that y'' +y=4tsint, y(0)=0=y'(0).  Here, the characteristic equation is m2+1=0⇒m=±i.…

Q: psin(rx) (b) Let g(æ) 1 and f(x) g(t) dt. Find f'(2). x4 + 1

A: We have to use derivative under the functional limit formulae first then put x=2.

Q: Let F(x): V t2 + 3 dt. Find 1 (a) F(1) = (b) F'(1) = (c) F"(1) =

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Q: Draw the bifurcation diagram for dy/dt = y(a-y)

A: We can use concept of critical points in order to solve the given problem.

Q: Let 3x3-y3 = 2. What is the value of dx/dt if dy/dt = -2 when x = 1?

A: To find the derivative of x with respect to t.

Q: y(t) = d²y dt² - dy dt 4. - 5y = 0, y(1) = 0, y'(1) = 3

A: we are given a differential equation and we need to find its solution.

Q: Find dx dt dx dt || at x = 5 if y = 4x² - 4 and dy dt = 3.

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Q: a) Write the initial value problem in vector form. b) Solve by using eigenvalues/eigenvectors. c)…

A: Given -  dxdt = x - y , x0 = -1dydt = 5x + 5y , y0 = 1 To find - Write the initial value problem in…

Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: t² - t dt 0, = (x)6 g'(4) =

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Q: Let f' (t) dt = 9 and f (2) = 3. Find f (6).

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Q: dy = 1+y² dx y' = yx³

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Q: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-1

Q: So Væ' (t)² + y' (t)² dt = 0.

A: Given data:     The given expression for the integral is:.   The given integral can be written as,…

Q: Dy/dt = 2y(5-y) is the equation autonomous?

A: An autonomous equation is a differential equation in which the independent variable does not appear…

Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

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Q: Find dx dt dx dt at x = −5 if y = −4x² – 5 and dy dt = -4.

A: y=-4x2-5given  dydt=-4d dx(xn)=nxn-1d dx(constant)=0

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: dy/dt = y(1-y) y1(0) = 9, y2(0) = -1 What do y1 and y2 mean? The first and second derivatives?

A: