(a) y.y-s (b) 2°z-2-4 z 'z (c)

Q: y" + 2y + 5y = t cos(5t)-6,y(0) = 1, y'(0) = -2

A: Here we use the table of Laplace transform and the partial fraction method to find solution.

Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

A:

Q: y = C,e²x cos(3x) + C2e2x sin(3x)

A: y=c1e2xcos3x+c2e2xsin3x  differentiate with respect to x…

Q: 41. e* sin y d A, R = [0, 2] × [0, 4]

A:

Q: || (2? + y*) cos(zy) dz dy? R

A: Here the Cartesian coordinates (x,y) are converted into (u,v) by substitution method as xy=u, x2-y2…

Q: e = (cos (y)+isin (y)) %3D O صواب İhi O

A: ez = ex+iy = ex (cos(y) + is in(y))

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: 1 (D2 – 3D+ 2) Y = cos²(e-²)

A:

Q: y" – 5y' + 6y = 10e' cos t, y(0) = 2, y'(0) = 1 %3D

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Q: y' + 2y = 3 sin(e2×)

A: y.e^(2x)=-3/2 cos(e^(2x)) + k

Q: b) Z = Arctan ( x² /y³)

A:

Q: + dy-39 sin ax y co) y'o) =12

A: Laplace transferom for the differential equation

Q: dy 2y ! = -x² y² sec²x %3D dx +

A: Using solution of Bernoulli Differential equation.

Q: b) y"+ 4 y = cos (t), y(0) = y'(0) = 0

A:

Q: D- y" + 2y' + 5y = 6e2* + x sin? x + e*cos 2x %3D

A:

Q: Find the solution of ordinary differentral equation X+2xy'-2y=L4xlox -5cos(Inx)

A:

Q: 1. Find y' a) y= X fanx In3 b) y= 3 <) y = (cos@)r2 %3D

A: Since you have asked multiple questions, hence we are solving the first question for you. If you…

Q: -dz , where y is given in the figure z2+1

A:

Q: y′′+ 4y = 32t cos 2t, y(0) = 0, y′(0) = 2

A:

Q: d²z et Ze2x Tan y Find- and dxdy d²z dydx

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Q: y= cos (1-t) and x=V2t - t2

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Q: #5 ở V - (2xy sinz) - (3y~); + (5x> y? z?)k .* and vx ů. ealeulate

A:

Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

A:

Q: (cos2y — Зx? у?)dx + (сos2y — 2xsin2y — 2x3y)dy %3D0 - |

A:

Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

A:

Q: y = 3 Arccos ( 1 -)+ v6x – x² %3D 3

A: To find the first derivative of y=3 arccos1-x3+6x-x2, use the sum rule of differentiation,…

Q: ZX = 24, XY = 10, and YZ 26. Find cos Y. %3D 5/12

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Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

A:

Q: (b) y = cos'(11x* + 2x).

A: Given y=cos511x4+2x use the chain rule of differentiation to differentiate the function…

Q: y'+y=e-6 cos St, y(0) = 0

A:

Q: cos(s) d u du = ds -8

A:

Q: d'y Solve d’y dy -6- dx? dx -+13y%3D8e"sin2x

A:

Q: SV1- x2 sin-1x dx

A:

Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

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Q: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

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Q: If y = cos24x, find dy/dx. a. 2cos4x     b. 2sin4x c. -4sin8x    d. -8sin4x

A:

Q: dy 7. Find ,y = cos³xsinx? dx

A: Given: y=cos3xsinx2 Formula used: Product rule of derivative: ddxf×g=dfdx×g+dgdx×f Power rule of…

Q: (d) (.9.z) = arctan(y/F) + sin (3 + ry-5y).

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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Q: y - 4y+ 4y = 2t2 + 4te2t + t sin2t

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Q: 25) y" + y = 2 cos(t), y(0) = 2, y'(0) = 0.

A: Use second order differential equation

Q: .y" +4y= cos x, y' (0) = 0, y' (n) = 0

A:

Q: b- y" -y+2y+ cos x, 05x y(0) -0.3, y()--0.1

A: To show the boundary value problem has unique solution we solve the given ode by method of…

Q: NOTE: Enter the exact answer. yz dx dz dy = %3D -90

A:

Q: y"+2y'+5y = 10 cos t, y0 = 2, y'0 = 1

A: Differential Equation: y''+2y'+5y=10 cos ty(0)=2,y'(0)=1The auxilliary equation…

Q: y" -3y' + ay = e when y Co) = y'Co):0 %3D %3D

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)],; it is defined as…

Q: y 3x+ 6 cosx, 0 £xs 2n

A:

Q: e/ (cos(2²) + y²) dæ + (sin(y²) + 2aæ²) dy Evaluate

A: In this question, we need to find the integral over C.  C is a closed curve with the boundary are…

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.