Solve the general solution y" + y = xex sin 2x

Q: dy 4. x - y = x² sin x dx

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Q: 2. Solve using any technique y" – 2y – 3y = sin r

A: First we find CF and then PI(by using the formula of PI of sin(ax)) and further find general…

Q: solve using the appropriate method. y' + (tan x)y = cos2 x, y(π) = 2

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Q: Solve the equation for x in terms of y if 0 < x < π and 0 < y < π.sin x/3 = sin y/4

A: An equation can be defined as a mathematical statement consisting of an equal symbol between two…

Q: find general Solution (D²+6D. Sin 4X to

A: Given differential equation is : D2+6D+16y=sin4x To find the general solution.

Q: (D² + 4) y = 4 cos³ (2x)

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Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2ex sin2(x/2)

A: Given the given differential equation is d2ydx2-2dydx+4y=2exsin2x2

Q: y''-5y=sinx

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Q: Solve using the Method of Coefficients: y'' + 3y' + 2y = 7 cos x - sin x

A: The given differential equation

Q: Q Is the equation e + x cos x 2 = 0 has real roots?. -

A: To show there are real roots, just use intermediate value theorem on appropriate interval.

Q: dy (b) Solve the initial value problem = 2 sin 2x – 3 csc² x, dx = 5.

A: We can solve the given differential equation by using variable separable method.In this method…

Q: b. y= 2 sin 2x+1

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Q: Solve the stated IVP using the method of undetermined coefficients.   y’’ + 3y’ = 3 sin 2t, y(0) =…

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Q: Find the general solution to y" +y = x sinx

A: We are given second order non homogeneous linear differential equation with constant coefficients.…

Q: Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: Find the general solution of the equation: y' -2y = 2 sin(3t).

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Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

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Q: Solve (D2+1)y = sin x sin 2x %3D

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Q: Verify that (e* sin y +3y)-(3x- e* sin y)y' = 0 is exact. Then solve the equation. 5.

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Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: Solve each of the equations. Integrating Factors (y +y cos x – ye*) dx + (3x +3 sin x – 3e*) dy = 0;…

A: Given: y+ycosx-yexdx+3x+3sinx-3exdy =0; y0=-1 ⇒1+cosx-ex3x+3sinx-3exdx=-1ydy

Q: 1. Solve the linear equation y' +y = 5 sin 2t.

A: Given that  y'+y=5sin(2t) To find the general solution of the differential equation

Q: Solve linear DE  (D2+2D+2)y=e-x+sin2x

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Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

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Q: 4 Find (b) y sin 2x.

A: This question is about differentiation or finding derivative of y with respect to x.

Q: 5. Solve the equation (D + 1)y = sin x

A: 5 ans

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

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Q: solve linear DE (D2+2D+2)y=e-x+sin2x

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Q: 3. In the equation y = sin1 x, if x = 0, then y = 0.

A: We have to use the inverse sin function and the interval -π2,π2. We have to recall the trigonometric…

Q: Find the general solution to the equation: y' = y sin(2x + 3) .

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Q: dy Solve sin -1 | = x +y dx,

A: Sin-1(dy/ dx) = x+y => dy/ dx = sin(x+y).

Q: 2:Solve: cos (x+ y) dy = dx %3D

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Q: Find the general solution of y" – 4y' + 5y = sin (x)

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: Construct an equation such that y = = C1e3z cos x + C2e3ª sin x is its general solution.

A: To determine the differential equation from the solution  Check the number of constant in the…

Q: che general solution of -V - 6y = 6x3 + 26 sin 2x

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Q: IV. y-y=sin x+cos 2x +e

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Q: Solve the ODE: (7e sin y – - 49y sin(7x))dx + (e“ cos y + 14y cos(7x))dy = 0

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Q: (27) Solve (1+y²) | n = (tan'y-n)·dy

A: The general solution geometrically represents an n-parameter family of curves.

Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

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Q: The solution of Sinx dx - x sinx+ y cosx= 0 is (y– 1) sinx =? A C-x sinx B C+ x cosx с-х cosx D C+ x…

A: sinxdydx-xsinx+ycosx=0sinxdydx+ycosx=xsinxddx(ysinx)=xsinx

Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: Find the general solution of: y"-3y 8e* + sin 2-

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Q: Solve the equation: dy (4x + 5)2 1 tan x · Y = 2 ,3 dx 2 cos x

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Q: Solve by Bernoulli's Equation 2. sin y(x + siny)dx + 2x?cos y dy =0

A: We find the solution by Bernoulli’s Equation.

Q: 2. Solve the DE: 2y' - y= 4 sin( 3x)

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Q: Find the general solution of the equation y" − 4y' + 3y = sin(x)e²x -

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Q: Solve the ivp y′=sin^2(x−y)    y(π/2)=π4 Solution is y(x)=

A: Given,

Q: e-3t sin (4t) y (0) ==

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Q: Solve by variable separable method: dy/dx = x^2 + cos 2x

A: Given, The differential equation, dydx =x2 +cos2x  We have to solve the differential equation by…