The answer to this equation is y = (1/5)e^x + {(1 – (2/5)sin x – (6/5)cos x}e^–x y" – y = 2e^–x (cos x – sin x), y(0) = 0, y'(0) = 0

Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: Can we solve following differential equation by separable variable method dy y = eV+sinx secx %3D dx

A: Given differential equation is as follows : secxdydx=ey+sinx……1 Let Fx,y=dydx If Fx,y can be express…

Q: Find the intergration of x^3(x^4-sine)^5 dx

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Q: Solve the differential equation by variation of parameters. y" + y = sin?(x) sinx ( sin’'x cos (x) +…

A: Solve the above questions

Q: 12. cos cos (xy) = 1+ sin y

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Q: and dr= %3D Solve for the differential of y When y=sinxx x

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: Date: an ordinary By using suitable method differential equation by eliminating from the equation…

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Q: Find dy/dx of y = cos^-1(2x) * sin^-1(2x)

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Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: Find the differential equation characterizing the family of curves described tangents to ky = x^2

A: We need to find the differential equation characterizing the family of curves described tangents to…

Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

Q: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

Q: 4. S(cos 2x)e$in 2.x dx 5. S cos x In(sin x) dx 6. ſ tan 0 In(sec 0) de

A: According to given : Only 4,5,6 are solved

Q: Obtain the differential equation of the family of circles of fixed radius r with center on the…

A: We have to obtain the differential equation of the family of circles of fixed radius r with center…

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: (2y cos x + sin*x) dx = sinx dy %3D

A: Given, Differential equation : 2y cos x+ sin4 xdx=sin x dy To find: General solution of given D.E.…

Q: solve for exact Differential Equation (ex + ln y + y/x)dx + (x/y +ln x + sin y)dy = 0

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Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: Find dy/dx of y=sin-(1/,). 9x-

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Q: integral of cos 2x e sin 2x dx?

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

Q: Find the first derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and y = ( ex – e –x ) / (ex…

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Q: 3. x)dx sin(ln

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Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

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Q: The integrating factor of the linear differential equation – (tanx)y = x is_ - O sinx O log(cosa)…

A: Given dydx-tanxy=x

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: We know sinh xcosh x = tanh x ∫tanh ax dx = 1alncosh ax + C    (where C is constant of integration)

Q: Evaluate the integrals

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: 54, y = (ln x)cos* cos x %3D

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Q: 2.Find , if y = sinh x %3D dx' 1+cosh x

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Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: Find dy/dx by implicit differentiation 4 cos (7r) sin (6y ) 5

A: We have been given an implicit function and we are supposed to find dy/dx.

Q: 1 3), sinh(x)-cosh(x) dx

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Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: Find dy/dx 1. y = sin ( 5x - 9) 2. y = sin-4x/5

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Q: Solve differential equation (2y cos y - x sec y - x tany)dy = (1 + sin y) dx

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Q: Find dy/dx by implicit differentiation. 5y sin(x2) = 9x sin(y2)

A: Given :  5y sin (x2) = 9x sin (y2)

Q: Find dy/dx by implicit differentiation. (cos TX + sin ny)³ = 26 dy/dx =

A: Differentiate above equation with respect to x

Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: Given the non-exact differential equation (ysin(x) + cos(x) )dx + (x+y)sin(x)dy = 0. Find the…

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Q: dx =?

A: we have to solve integration

Q: E PARTICULAR SOLUTION OF EVERY EQUATION GIVEN. [tan y – (In x)°]dx = 0 When:x = 1; y = " 4

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Q: how do i implicitly differentiate (solve for dy/dx) where: xy = tan(xy)?

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Q: 1 dx cos² 2x 3. 4. x² sin (x³) dx S elnvx+1 dx 5.

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Q: Find the differential equation of the family of circles with fixed radius and tangent to the x axis.

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Q: Find the differential equation corresponding to y=acos(logx) +b sin(logx)

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Q: (1) | cosx In (sin x) dx (2) [ xe -TX | хе dx x (3) x -16 dx

A: As per guidelines, we are supposed to solve only first two questions. Please repost other questions…