Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the complementary equation sin(x)y''+ (2 sin(x) – cos(x))y' + (sin(x) – cos(x))y = e=² OS Y1 = e-, 2 = e cos(x) COS Yp(x) = %3D

Q: (b) у" — 2у + у 3 еt sin(z)

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Q: Solve (sin(x) cos(y)) dx + (cos(x) sin(y))dy = 0 if possible. If the equation is not exact, say so.…

A: First we check given differential equation is exact or not.  If given differential equation is exact…

Q: x*cos(y/x)*dy/dx = y*cos(y/x)-x   find solution of that differantial equation.

A: Let us consider the differential equation of the form dydx=fyx  then to solve the differential…

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Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

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Q: Use the variation of parameter method to find a general solution for the variable coefficient…

A: Given That : differential equation  y"+2tan(x)y'-y=0 ,0<x<1 To find : use the variation of…

Q: 3-(cos x)y' =yCv-1) sin x.

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Q: Use variation of parameters to find a particular solution, given the solutions y 1, 2 of the…

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Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: Solve the equation y' (t) + y(t) t dz -√4(z) Sin (t-2) d2 = - Sint yco) = 1

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Q: 5cos³(x) sin(3–2x) answer in terms of sin and cos only ind the derivative of y = + tan²(3x² – 4x) –…

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Q: 2. Solve 3 y'(z) + y(x) = y²(z) (cosz - sinx)

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Q: y′= (6xe^(6x)) X (cos^(2) (6y)) a) Write the equation in an integrable form by separating it into…

A: Solve using variable separable method.

Q: The solution to the equation is * y'(x)- 2y'(x)+ y(x)-cos(x) slad Ja sin(x) - y(x) =c,e" +e,xe"…

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Q: (cos(2x) – sin(2x)cos(2x)) cos(x) – sin(x) For -dx=-F(x) + C. What is F (x)? 3 A (csc(x) – sec(x))3…

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Q: y (3, 4) sin(0) = %3D cos(0) = tan(0) = csc(0): sec(0) : cot(0) = %3!

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Q: Solve by variation of parameters method (h) y" + y' = tan x

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Q: Solve y' = cos(2x + y – 5) – 2. = COS

A: The solution is given as

Q: s to find a particular sy1, y2 of the s(x))y'+(sin(x) - cos(x)) y = e 2 = e-* cos(x)

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: In this particular problem, where is the u and du? Why does it suddenly not present in the solution?…

A: the given integral is: ∫esec(x)sin(x)cos2(x)dx let the given integral be I.…

Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: Solve the equation y' = csc(x) - y cot(x).

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Q: Find solutions using Exact Equations 1. Solve (y sin x + xycos x) dx + (x sin x + 1)dy = 0 2. Solve…

A: As per guideline , we can solve only one question at a time. If you want another question to be…

Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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