Q1/ A: Find: 1 L-1 55+4 2S-18 5²49 24-30 √S + 54 2- L (t² cos at)

Q: 2.2 y = (x³ − 1)(x² − 2x + 1) using the product rule. √1 + tan² x 2.3 y= sec² x

A: solution of the given question is like aS:

Q: Express these functions either in terms of a cosine term only and as a sine term only or expand to…

A: Note:-  cosA-B =cos A cos B - sin A sin BsinA+B =sin A cos B + cos A sin B   Part (1):- Given that…

Q: Given α+ßi = √¹x³¹_x=¹¹dx, Inx 0 α, ß ER, find the analytic expressions for a and

A: Recall the following formula  ln(a+bi)= ln √(a²+b²) + i tan-1(b/a) .

Q: Solve using the method of indeterminate coefficients. q''−4q'−21q=5e-3t

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Q: Ex:. Find the fourth roots of Z=-di Say no 4 K = 0₁12₂3

A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: [X] Evaluate √ 1 √9+x² 2 dx

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Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: The tanh (2x) sech (2x) dx is equal to sech (2x) sech (2x) +C OA 3 10 OB. sech (2x) sech (2x) +C. 3…

A: Solution

Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: (2x + 1)(x – 1) dr 9. 3x + 6 d.x 2.x3 10. | (20 – 1)(x² + 5)dx 17. - (3x – 2)2 - 18. 4x

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Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: (b) I cos cos(√x + 3) dx

A: b Given integral is ∫cosx+3dx. We have to solve the given integral. Use formula…

Q: Determine the form to be used for x when using the method of undetermined coefficients. x" + 2x = 8…

A: Given DE is  x"+2x=8sin(2t) ......(1)

Q: Differentiate the following:

A: Step 1:Step 2:Step 3:Step 4:

Q: Determine for which values of m the function (x) = xm is a solution to the given equation. d²y dy -…

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Q: find the general solution - こ (64y = sin (2x)

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Q: BEC zw. w-1 (iii) Arg w and arg w. -√3i. Find the following: Let z = 7+3i and w = -1 –

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Q: b) Show that P1(cos(0)) and P2(cos(0)) are orthogonal to each other, P, and P2 being Legendre…

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Q: If = {(x, y) | 16 ≤ x² + y² ≤ 49} then: 11.000 = [ co cos (x² + y²) dA

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Q: Find the complete solution: (cos2y - 3x²y²)dx + (cos2y − 2xsin2y — 2x³y)dy = 0

A: Given data:  cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0 We have to find the complete solution.

Q: 4.a) Find d dx y = ln (2²/ n (²x + 5) b) Find dy dx y = 3√√x++2x e³x (5x²)

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Q: then dy dx y = tan -1 ¹ ( √7x² − 1),

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Q: 1. a) Find , if y= (x² – 11)“ dx b) Express (8/30) (2Z60) in the form a+ bi c) Solve (2+3) +3/- x+iy…

A: The detailed solution is as follows below:

Q: 5. 1/2 cos² Itsin -dx ANSWER: л/2-1

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Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: (iv) |z − w|. (v) ws. Let z = 7+3i and w=-1-√3i. Find the following:

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Q: y = x³+4x-15 y = x² cos x y=tan(x/3) at x =0 at x=0.4. at x = 3

A: Since you have posted multipart question  i have solved the first three question as per our company…