Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 17y = 0. Separate your ans by commas.

Q: Verify that the function y = 6x − 4 sin x + 1 is a particular solution of the differential equation…

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Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: State the order of the given ordinary differential equation. (2x - tan(17x))y"" - x²y" + 18y' =…

A: Given the ordinary differential equation is  2x-tan17xy'''-x2y''+18y'=18sinhx+16

Q: Determine whether the function y = 3 cos 2x is a solution of the differential equation y(4) − 16y =…

A: y = 3 cos 2x We need to check whether the given function is the solution of the differential…

Q: determine the general solution of the given differential equation that is valid in any interval not…

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Q: Verify that the given function y = sin (x2 + C ) is a solution of the given differential equation:…

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Q: 2. Obtain the Differential Equation from the given general solution. y = Cj cos(3x) + C2 sin(3x) +…

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Q: Find the value of k so that the differential equation (6ry³ + cos y) dr + (2kz²y² – 1 sin y) dy = 0…

A: we have to find the value of k when the given equation is exact            (6xy3 +cosy)dx…

Q: Obtain the differential equation whose general solution is y =a sin 6x- bcos 6z, where a and b are

A: Given: y=asin6x-bcos6x for finding differential equation for given equation, we have to eliminate a…

Q: c. y" +4y=tan2x %3D

A: Solution of the given differntial equation is

Q: Evaluate the given differential equation (3siny – 5x)dx + 2x°coty dy = 0

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Q: For the differential equation x ^ 2y ”+ xy’ + y = 0, check that y1 = cos (lnx) is a solution. Find…

A: According to the chain rule of differentiation, the differentiation of the composite function…

Q: Use Frobenius method to find the first three non-zero terms for the following differential equation:…

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

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Q: Find a particular solution y, of the differential equation: y" + 9y = 2 cos 3x + 3 sin 3x

A: Explanation of the answer is as follows

Q: y = c, sin wt + c2 cos wt

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

Q: The standard form of the differential equation cosx y' + cosx y = x sin x is: None of the above O…

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Q: Consider the differential equation x¨(t) + x(t) = 5t2 − 2 cos 2t.  Write down the ansatz for xp…

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Q: Find the differential equation by eliminating the arbitrary constant/s. Gedr cos x + Cge y = c1e 3x…

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Q: Verify if the given functions are solutions of the differential equation. Also, determine the value…

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Q: determine the general solution of the given differential equation that is valid in any interval not…

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Q: Form the differential equation for the function x+2y=a sin3x-bcos3x

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Q: Find the curve y that satisfies the differential equation y' sin r and passes through the point (T,…

A: Integrating the equation

Q: a. y = 3 sin 2x+ e-* ;y" + 4y = 5e-*

A: y=3sin2x+e-xAnd y''+4y=5e-x

Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

Q: Find the solution of the differential equation dy = cos(5x) Vy dx which satisfies the initial…

A: y'=cos5xy dydx=cos5xy dyy=cos5xdx y-12dy=cos5xdx take integration

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation is dx=x9y dy. Rewrite this as y dy=dxx9.

Q: what is the particular solution to the differential equation dy/dx=3sin(x)(2-y)with the initial…

A: You need to apply variable separable metod to solve the given differential equation.

Q: Obtain the differential equation whose general solution is y= a sin 2x b cos 2x, where a and b are…

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Q: Find the value of k so that the given differential equation is exact. (7xy³ + cos(y)) dx + (2kx²y² -…

A: Given

Q: verify that the given functions are solutions of the differential equation, and determine their…

A: Differentiate y=1 with respect to x. y'=0 Differentiate y'=0 with respect to x. y''=0 Differentiate…

Q: Use the method of undetermined coefficients to find a particular solution to the differential…

A: Explanation of the answer is as follows

Q: Show that the function y=ex(sin2x+cos2x) is a solution of the differential equationy′′−2y′+5y=0.

A: We find the first two derivatives of y using the product rule

Q: Show that the differential equation [y(1+1/x)+cosy]dx+[x+lnx-xsiny]dy=0 is exact.Hence solve it

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Q: Use the method of undetermined coefficients to find a general solution to the differential equation:…

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Q: Find the solution to the differential equation that satisfies the stated condition. sin (5x + T),…

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Q: 2 sin²2t dx = cos x (1 + cos 2x) dt

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Q: sin(ax)y = -a cos(a.x)y + a

A: Given that  The differential equation  To find the general solution

Q: Find the value of n that makes the differential equation xn (3x+4y)dx +(2xn+1 +2y)dy = 0 exact.…

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Q: Solve the non-Linear differential equation dy Cos y de sin y(1 – 0 sin y),given that y(0) = 8.

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Q: Solve the differential equation as follows: (6xy* – sin x tan y)dx + (12x²y³ + sec? y cos x – 5y²)dy…

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Q: Solve the first order differential equation using any acceptable method. sin(x) dy/dx+(cos(x))y=0,…

A: We have given First Order Differential Equation,

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

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Q: dy 47. = cos cos 2x, y(0) = 3 dx

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Q: Verify that the function y (cos( 6x)) is a solution to the differential equation y = 6 sin(6 9e

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Q: 手u等() dy dy seex dy-o 2 csey dx+ secx dy-o

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Q: Find the differential equation by eliminating the arbitrary constant/s. e COsX = c(1 – cos y) %3D

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Q: Verify if the given functions are solutions of the differential equation. Also, determine the value…

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