(b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

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Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: |x In x dx 2. x3e3x dx 3. tan-1x dx / e* cos 3x dx 4. 5. fx*sin 3x dz Scos"1. Vx dx 7. sec-1. Vx dx

A: I have solved first three parts  For other parts please repost question It's bartleby guideline

Q: Find the differential dy of the given function. y = In√9-x² dy =

A: Given y=ln9-x2 Formula: ddx(ln u)=u'u where u is a function of x Now consider y=ln9-x2 The given…

Q: find a linear differential operator that annihilates the given function. y = x sin(3x)+ 3xe6x

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Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: 2. (2.xy – sin x}dx+ (x² - cos y ldy =

A: We will solve the given differential Equation.Below find the solution in the image.

Q: 5. x- + Px = sin t %3D dt

A:

Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

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Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: 2 (b) - 2y dx +(2y tan'(x )-2x +sinh (y))dy = 0

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Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: Find the differential dy of the given function. y = In√√/9-x² dy =

A:

Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

A:

Q: Show that a harmonic function u (x, y) satisfies the formal differential equa- = 0. azdz

A: Consider the provided question, Given, ux,y is harmonic function. We have to show that ∂2u∂z∂z¯=0.…

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: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

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Q: dx + 3x = cos(5t) dt with x(0) = 1. x(t) = %3D

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Q: x²y' + 2xy = In x, У(1) 3D 2

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Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

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: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

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Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

A: The given initial value problem is: dxdt+3x=cos(5t) ;         x(0)=1

Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

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Q: Find the number N such that the differential (y^3-2x)dx+Nxy^2dy is exact

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

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Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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Q: 18 -14 dx dt 21 -17 with the initial value x(0) %3D 9 x(t) LO

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Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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

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Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…

Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

A: