Consider the D.E. y(ª) + 4y" = 1 – cos(2x). Then a suitable form of the particular solution can be written as yp(x) = (A) Aa + a[B cos(2x) + C sin(2x)] (B) Aa? + a[B cos(2x) + C sin(2x)] (C) Aa? + B cos(2x) + C sin(2x) (D) Ar+B cos(2x) + C sin(2x) (E) None

Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: Find the solution of the given initial value problem in explicit form. 75 ㅠ sin (2x) dx + cos(7y) dy…

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Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(8y) dy =…

A: Let's solve given diffrential equation.

Q: 1. Show that y(x) = c; sin 2x + c₂ cos 2x is a solution to y + 4y = 0.

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Q: 3. Find the general solution of y" – 3y + 2y = cos (e~-).

A: We use the method of variation of parameters to find the solution of y''-3y'+2y=cose-x First we find…

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

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Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

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Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

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Q: Find the particular solution of (cos x x sin x + y2) dx + 2xy dy = 0 that satisfies the initial…

A: Please see the explanation below

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(6y) dy = 0,…

A: The given initial value problem in explicit form is sin2xdx+cos6ydy=0, yπ2=π6. Find the solution of…

Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

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Q: Solve the initial value proble = sin (5x +x), y=3 whe OA. y= 1 cos (5x +x) O B. y= - cos (5x + x) +…

A: Given: dydx=sin(5x+π)y=3, when x=0

Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: Solve the initial value problem (dx/dt)+2x=cos(4t) with x(0)=−2. x(t)=?

A: Solve the initial value problem

Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

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Q: 7. Obtain the solution of (D² – 4)y = 16 + cos 2x using the method of undetermined coefficients %3D

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the solution of the given initial value problem in explicit form. π sin(2x) dx + cos(9y) dy =…

A: Given: Now,                sin(2x)dx+cos(9y)dy=0Integrating both sides we…

Q: Find the general solution of y" – 3y' + 2y = cos = COS

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Q: How can I find the particular solution of y''+36y=cos(6x)

A: How can I find the particular solution of y''+36y=cos(6x)

Q: 5.. Find the general solution to the DE using the method of Undetermined Coefficients: y" – 4y = te'…

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Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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Q: Find the particular solution of the nonhomogeneous ODE. y"-4y' + 3y = x² + e* + sin2x

A: We will find out the required particular solution.

Q: (b) Find the solution for cos(x) − (1 + x²) x − 2xy = - - with the conditions y(1) = -1, y(2) = 2…

A: Note:-  For this problem if you want general solution for this problem then please resubmit problem…

Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 2 cos 5x. a2. - 00 0, u(x,0)…

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Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

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Q: Find the solution of the given initial value problem in explicit form. sin(2x)dx+cos(6y)dy=0,…

A: Our objective is to find the solution in explicit form.

Q: The solution to the initial value problem y" + y = 8 cos 2x – 4 sin x, y () = -1,y () = 0 is y = -n…

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Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

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Q: Find the general solution of the d dy 2c-2v = dx 3 sin(x/2)√ √cos³(x/2)

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Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: 2. Solve the initial value problem f"(x)= 2cosec3xcot3x +5 cos(-x)+3, given Зл = 4 4

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Q: Find the solution of the given initial value problem in explicit form. π ㅠ sin (2x) dx + cos(7y) dy…

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Q: Find the solution of the given initial value problem in explicit form. 71 ㅠ sin(2x) dx + cos(6y) dy…

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Q: Solve the initial value problem dx 2x = cos(4t) dt with x(0) = 1. x(t) = sqrt(-1/4sin(4t)+1)

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Q: Find the solution of the given initial value problem in explicit form. 7 ㅠ sin (2x) dx + cos(7y) dy…

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Q: Solve the initial value problem. dy + y sin x = 2x cos² x, dx y(0) = 0 COS X - 2.

A: Given: cos(x)dydx+y sin(x)=2x cos2(x)

Q: Find the solution of the given initial value problem in explicit form. sin (2x) dx + cos(7y) dy = 0,…

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Q: Find the general solution of the DE: dyldx = sin(7x) cos(5x) + cos(7x) sin(5x). O y = (-1/12)…

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Q: Find the solution of the given initial value problem in explicit form. 75 π sin (2x) dx + cos (7y)…

A: The given initial value problem is                        sin2xdx+cos7ydy=0,  yπ2=π7 We have to find…

Q: 3. Find the general solution of y"-3y'+2y = e* cos x [using variation of parameters]

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

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Q: Solve the initial value problem dx/dt + 4x = cos(4t) with x(0)=-2

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Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

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Q: 4 Give the general solution to x²y' + xy = -2 cos(2x) y¯2

A: The solution is given as

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(7y) dy =…

A: Here we use basic integral to find the solution.

Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: Find the general solution of (x + y) cos ydr + (a cos y - sin y)dy = 0. |3|

A: Differential Equation: A differential equation is an equation that contains one or more terms and…

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.