Verify directly that the relation y = C3 e cos bx + c4e sin bx satisfies the equation [(D – a)² + b?]y = 0.

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Q: Evaluate [sin³ a x cos x dx. + C

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Q: Differentiate y = In (cos² 3x).

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Q: sin X 1/ガースゴ+スコービsinx

A: Given differential equation is  y" -3y' +2y=e^x sinx

Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: Find the roots of 3 cos (x)-x2=-10.

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Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: Identify whether or not the following equations are homogenous or non-homogenous /x² – xy tan…

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

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Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

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Q: Solve for the convolution of sin (t) and cos (t).

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Q: A total of 2 freshman, 3 sophomores, 4 juniors and 5 seniors have been nominated to serve on a…

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Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Evaluate: D°(sin x- e20) A -sin x - 32e* B sin x - 32e2 © -32- e D cos x - 32e2

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Q: y = cos(x),

A: Given data:     The given function is: y=cos(x).       (a) The cosine function is an even function…

Q: Find the value of A. (A-B+C) + (2A + B) sin (2y) - (2B - A) COS (2y) = (4+j3) (6-j2) sin² (y)

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Q: y = cos(-4x)

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Q: Find an equation such that y xe" cos(2x) is its solution.

A: To find an equation we derivative both side with respect to x.