(Q6) Solve the following non-linear algebraic equations: (a) 2ex + sin 2y + 22 5, sinhx + 22+1 2sin y cos y = 10- cosh x, e +2 sin 2y + 22 = 3 %3D

Q: Solve the initial-value problem y"– 4y = e" cos r, y(0) = 0.7, y(0) = -1.5. %3D Answer: y(x) = %3D

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Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: Find the exact solutions of vZ sin (x -)+ 1 = 0 for 0 sxs 47.

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Q: se the method of undetermined coefficients to find the general solution to: y'' + y = 5 Cos(t)

A: Use the method of undermined coefficient to find the general solutionof differential equationy''+y=5…

Q: Find the particular solution : y" + y" +4y sin2x sin2x (b) Yp =sin2x (a) yp = - (c) Yp =- cos2x ()…

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Q: 8. Find a particular solution yp(x) to the equation y" +y' – 2y = 5 sin x in the form yp(x) = c1…

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Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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

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Q: (x²-cos(2x). c. T(x) = x d. T(x) x2. find Q at x = t/4. = 100e-3x + In(4x), k=470, A= 0.01r and x=…

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Q: What is the solution of the D.E y"- 3y' = e* sinx when solved using the | method of undetermined…

A: We need to find the solution of the given differential equation using the method of undetermined…

Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: HH F Solve the following equation with undetermined coefficients. What are the coefficients of the…

A: The detailed solution is as follows below:

Q: Find the complete solution of yn+4y=ex sin2x

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Q: 2x Show that y = e²* sin 3x satisfies the equation y"-4y'+13y=0.

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Q: Q7// find the general solution 1 (sin-ix + =y)dx + sec-1xdy = 0 xVx² – 1

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Q: Find the general solution of the following equations. 4. dy - x² = x dx sin x 5. y-'dy + ye cos x dx…

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Q: 3. Find the general solution of y"-3y'+2y = e2* cos x [using variation of parameters]

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Q: The equation below is said to be 3 dy (x² – 1) \dx, sin x — х - + ye2x+1 %3D O A. Linear and…

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Q: 1-cos (t) B: Solve the D.E ý + 2ý + y = with zero initial conditions

A: Given y''+2y'+y=1-costt2with zero initial condition, i.e. y0=y'0=0

Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

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Q: Find the solution of the equation M a²z a²z = e cos y Əх² ду? which tends to zero as x→∞ and has the…

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Q: Determine Yp using undetermined coefficients: 2. (D2-1) y = e-x (2 sin x + 4 cos x)

A: The solution of the problem is given in the next step.

Q: The equation below is said to be - 1 attachment - (d²y' 3 (dy sin x – x (x² – 1) ( + ye2x+1 dx2 dx,…

A: Given D.E

Q: Find the general solution of the equation: y" - y' - 6y = exp(-x) - 7 cos x %3D

A: We find the general solution of  y"-y'-6y=e-x-7cos(x).....(1)

Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

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Q: Q2) Find approximate solution up to 0(e*) for the equation 1) x - 2 + eex = 0 2) x + ev 2 +r = cos e

A: As indicated clearly in your question post, you want help only with the second part of this…

Q: 4. What is the form of y, given (D² + 9)y = x + tanx? A. Yp = V,sinx + vzcosx B. Y, = v, sin3x +…

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Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y +4y=x-2 cos 2x,…

A: The solution is given as

Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: Find the solution of the equation 22 J²z Əz + =e cos y dx² Əy² which tends to zero as x→∞ and has…

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Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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

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Q: dy - = 4 sin 2.x – 6 csc² x, y dx (b) Solve the initial value problem =7.

A: Just I have used the method of Variable - seperable and easily solved the given differential…

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: solve the nonhomogenous equation y''' - 6y' = -cos(x)

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

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

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Q: Q6// Solve the equation: y cos2 x dy + sin x dx = 0.

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Q: 1- y" - 6y' - 7y 2 cos Dt sin Mt Find Particular solution

A: It can be solved by finding C.F. and P.I

Q: 3. Find the general solution of y"-3y'+2y=e2* cos x [using variation of parameters]

A: See solution below

Q: 8. Find a particular solution y,(x) to the equation y" +y – 2y = 5 sin r - in the form yp(x) = c1…

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Q: Find the solution of the equation P №²₂ a²z อ + cos y ax² ay ² which tends to zero as x→∞ and has…

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

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Q: Use Newton-Raphson method to solve the following simultaneous nonlinear equations assuming x(0) =…

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Q: 4. y"+2y'+2y=e* cos x 3t 2.x"-2x'–4x = 2e" 27 6. x"-4x'+4x= te" %3D 5.

A: See the attachment.

Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

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