y' + y² = 3y tan x tan? x + 1

Q: find the general solution of the first-order linear differential equation. y' + (tan x)y = cos x

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Q: Find the general solution of the given differential equation and use it to determine how solutions…

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Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

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Q: Assume that the rate of change of y is proportional to y. Solve the resulting differential equation…

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Q: Find a function of the differential equation: y = x²-2 sin x

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x=(0, π). is:

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Q: Find the general solution of the differential equation. y′ = arctan x/ 2

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Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: Use the initial condition to find the particular solution of the differential equation. dy = 4xy…

A: In the given question apply the variable separable method, i.e, isolate the y terms on the left side…

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied 1 sin 2 1…

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Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: dy + ( 1+x)y = e -× sin2x dx

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Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

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Q: Obtain the general solution of the given differential equation: tanydy = sin3xdx

A: The given differential equations tan2y dy=sin3x dx⇒sec2y-1 dy=143sinx-sin3x dx    As…

Q: solve the differential equation. tan2 y dy = sin3x dx                   when y(0) = 0

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Q: Assume that the rate of change in y is proportional to y. Solve the resulting differential equation…

A: Given  dydx=ky Points on the curve 3, 3 and 4, 6

Q: find the general solution of the first-order linear differential equation. y' + y = ex

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Q: Find the differential equation by eliminating the arbitrary constant  sin-1x + sin-1y = c

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Q: A solution for the differential equation is y = eux A1 sin (vx) + A2 cos (vx), where m and n are…

A: We will find out the required values.

Q: Determine the solution to the differential equation given by: y''-2y'+y=sin x

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Q: Find a particular solution yp of the nonhomogenous differential equation y(3) + y' = x sinx + x²e* +…

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Q: Find the general solution to the differential equation using undetermined coefficients. y" + 5y =…

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Q: The differential equation formed by eliminating a and b from y = ae* + be* is

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Q: y' + (2 tan x)y = - cos'x

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Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: Find the solution for the second order differential equation y-4y = x sinh x.

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Q: y" - y = e2* - sin x

A: The given question has been solved in detail

Q: xcosydy + sin2ydy – dx = 0

A: First arrange it in the bernouilli equation then find its integrating factor. Then  use the formula…

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: What is the particular solution to the differential equation [x+(1+x)y] = 12 with y = 0 and =0 when…

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. ecosx = c(1-cosy)-¹

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use the method of Undetermined Coefficients to find a PARTICULAR SOLUTION to the differential…

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Q: Find the Differential equation by eliminating the arbitrary constant  Sin-1 x + sin-1 y = C

A: sin-1x+sin-1y=C

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: general

A: Please refer to the image below

Q: Find the general solution of the differential equation using any method          y′ = √( 1 − cos )

A: Find the generla solution of given differential equation y'=1- cos x

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: y" + y' = sect tan t

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Q: Determine the general solution of the given differential equation. y(4) + 2ylI + 2yl/ -x = 3e" + 2e™…

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Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

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Q: Find a function of the differential equation: y' = x3-2 sin x

A: topic - differential equations

Q: obtain the linear differential equation with the real, constant coefficients that is satisfied by…

A: Solution.

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin æ +…

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Q: Find the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

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Q: Determine the solution to the differential equation given by: y' + 2y = 4 cos x

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Q: dy_ y²sec² (-) tan (-) dx x2

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Q: y'tanxsin2y = sin²x + cos²y

A: Assume t=cos2y then differentiate both side with respect to x to find dtdx .…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.