ci. use laplace transforms to solve the inittial value problem: У' — y' – 3y = F (t), where y(0) = 0 and %3D (sint, 0

Q: Find the differential operator that annihilates x cos3x + x e³x sin2x.

A: Given equation is  xcos(3x) +xe3xsin(2x) we have to find the differential operator that annihilates…

Q: 4. Find f. (a) f'(x) = 1+3Va, f(4) = 25 (b) f"(0) = sin(0) +cos(0), f(0) = 3, f'(0) =

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Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: // sin(7x²) dx dy. Compute O y/3

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Q: Find dy/dx by implicit differentiation. sin(xy) = cos(x + y)

A: Given: sinxy=cosx+y Differentiate both side:…

Q: Find dy/dx by implicit differentiation. x Iny+y=xyó 6x5y6-In y dx x − 6x6x6 + y AP w 6x5y7-yhy-1 Á +…

A: The given function x ln y+y=x6y6. We have to find the derivative using implicit derivative.

Q: 5. (ex + Iny +) dx +(÷Inx + siny) dy = 0

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Q: |( + 3t) sin(2t) dt 13.

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Q: dy in each of the followi dx Find 1. x² + y² = a

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Q: Example: Show that the functions: x=- - sinh and y: sinh- V3 3 dy dx dy ii ) dt dx Taken together…

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Q: Let a > 1 be a constant and y = (9e- sin z 3) In(x+a). Find y'(0).

A: Product rule of differentiation:…

Q: Q3 Find dy/dx on the graph y3 sec /x2 + y2 = cos2x at point (1, 2).

A: We have to find the derivative  of given expression at point (1, 2)

Q: 1. Find the differentiation of the following functions with respect to x I. y = Jx3 + 5x – 7) II. y…

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: Integrate e* cos(x) dr COS

A: To evaluate: ∫02πexcosxdx To solve this we will use integration by parts

Q: POS jma- 3 d 1 sin t dt %3| dx 1 1 (A) – x sin(x²) (B) sin(x²) (C) x sin(x²) (D) –sin(x²) ов O O O O

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Q: 1. Find a differential operator that annihilates the function xe2 ( cos 3x + 3).

A: Given problem is :

Q: o(e) = La t -Va V1 + t²

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Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: cos(2t + 号) dt = e2t-3 寸 ト す

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Q: Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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Q: 2 sin x Verify whether the function g(x) =1- is the solution of the integral equation [1 – (7/2)]…

A: The integral equation gx-∫0πcosx+tgtdt=1 is a Fredholm integral equation. We have to check whether…

Q: Solve the following DE: [3sin (y) — 5x ]dx + 2x²cot(y) dy=0 Ox²[sin (y) - 2x]³=C'sin³(y) Oy³[sin(y)…

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