The function y=4 sin z satisfies the IVP: %3D y" +y = 0, y(7) = 0, y (7) = -4. Select one: O True O False

Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

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Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? Select the…

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Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: Find the particular solution of 3 In x sec y dx – 5x sin? y dy = 0 given y(e³) = 7 %3D

A: Topic :- Differential equation

Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: b) Solve by using Runge-Kutta method to find y,. dy = x + cos(y) ; 0Sx<1 ;y(0) = 1; h = 0.5 dx

A: Solve the intial value problem, using Rung-Kutta method

Q: f(x, y) = log, (3x) fe dy In(3x)/(yln(y)2)^2 ||

A: Topic- partial differential

Q: The linear approximation at x = 0 to sin(9x) is A + Bx where A is: and where B is:

A: Given fx=sin9x Differentiate fx=sin9x with respect to x, we get f'x=ddxsin9x=9cos9x Hence,…

Q: 2.f(t) = cosh wt sin wt

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Q: + Use Separation of variables to solve eくX<| Us co,t)こ0 I4 pts] ULx,0) = X

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Q: Q1: If Z = x³ + y* + (x sin y) + (y cos x), Find Zx/Zy?

A: We are given: Z=x3+y4+(x sin y)+(y cos x)To find: ZxZy This can be calculated as follows:

Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

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Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

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Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

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Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

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Q: of

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Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

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Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

Q: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: dy _ 2y = x-'y¯1 y(1)= 3 dx

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

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

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: The linear approximation at x = 0 to sin (7x) is A + Bx where A is: and where B is:

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Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

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Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y (0) = 3

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Q: 2.f (t) = cosh wt sin wt

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Q: r nosへSう'" ( メンン 2 COS(SIn (x))

A: Let, cos(sin-1x)=t⇒sin(sin-1x) 11-x2dx = dt⇒x11-x2dx = dt...(1)

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y ( 0) = 3

A: We can solve the given differential equation by using initial condition.

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

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Q: use the integrating-factor method

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Q: The linear approximation at x = 0 to sin(7x) is A + Bx where A is: and where B is:

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Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

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Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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