By using Laplace trans formations Solve : - -2X 2X +3 e Cos3X y(oJ=0, ýw=| %3D

Q: (c) x(t) = eat cos s wtu(t), a > 0 (d) x(t) = e-af sin w,tu(t), a > 0 %3D

A: Let xt is a function. The Fourier transform of the function xt is denoted by Xiwor Xf and defined by…

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = %3D (플) = 프2

A: Given:

Q: Evaluate the integrals

A: First of all use the trigonometric formula that is 1-sin2x=cos2x in the given integral to simplify…

Q: #21 2D Describe the motion of a particle with position as tvaries in the given interval

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Q: 2 2. L(sin 2x + e2x+3) = s2+4 s-2 Hint: e2x+3 = (e²2x)(e³)

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Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: find the speed at the given value of t. r(t) = (sin 3t, cos 4t, cos 5t), t =

A: Given: rt=sin3t, cos4t, cos5t To find the speed at the given value of t=π2. Solution: Speed is the…

Q: S₁ + Sa cos²0 de 01/2000 sin ²0 de csc ³0 de + Sc 01/se sec ³0 de The integral dx (x²+4)² can be…

A: We have to solve above integral

Q: A weight is attached to a spring suspended vertically from a ceiling. When a driving force is…

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Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: If an object is moving along a horizontal line, such that it's velocity, v(t) = cos(3t), what is the…

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Q: Let I = ,x? cos(x) dx. The approximation of I using the two-point Gaussian quadrature %3D formula…

A: The two point gaussian-quadrature formula  for numerical integration of integral, I=∫abfxdx…

Q: Laplace's equation reads vo = 0 %3D True False

A: The partial differential equation ∇2ϕ=0 is known as a Laplace's equation.Then ϕ is called harmonic…

Q: 3. The points where r = 1 – cos 0 and r= cos 0 intersect are (A) (0,0) (B) (0,0) , (C) (0,0) (D) (E)…

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Q: 3. The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given…

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Q: 2. In 00, AE is tangent to 00 at E, mZBCF =112 and mBE:mDE = 3:7. Find: (а) тBE (b) mZA E A В (c)…

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Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

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Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

Q: Find the principle solution of sec(4z) = 2. If there is a distinct solution from the other half of…

A: sinπ3 = 32 and  sinπ-π3=32 cosπ3=12   and   cos2π-π3 = 12 .

Q: 2. In 00, AE is tangent to 00 at E, mZBCF = 112 and mBE: mDE = 3:7. Find: (а) тBЕ (b) mZA E A C (c)…

A: In circle with center at O, we have following diagram We have to find (C) m<DEB

Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: az az Use the chain rule to find and as at sin(8) = r = st, 0 = s + t4 az %3D ds az %3D at Submit…

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Q: Solve the given intial value problem: COS I y + -y = y(x) = 0. %3D

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Q: cos?. z=1 s divergent or convergent?

A: Given series is ∑z=1∞cos2πz

Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: The equation (tan?x+3y?) sec?xdx+(3tan?x+y²)dy=D0 can be solved by A Bernoulli's Equation DE with…

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Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: A particular solution of the DE y" + y = tan (t) can be found by the method of undetermined…

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Q: cos? e + cose +1 = 0 [0,2m]

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Q: U + ru, =x u(z,0) = sin(87x) cos(90r). IE R, t> 0,

A: Given ut+xux=x2 By Lagrange's method , we get dt1=dxx=dux2 By equation (1) and equation (2) , we get…

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y<0 and we need to prove that | eiz | >1 For b part, we need…

Q: 3. 2.m (ris, t)= e cos (25) y= h(ris, t)- e sini (s) %3D + そ人メ+ (てん「以) =1 け! ne Use chain rule to…

A: Given, u=fx,y,z=x3+xyz+z2x=gr,s,t=e2rcossy=hr,s,t=e2rsinsz=mr,s,t=ercos2s To find: ∂u∂s Formulas…

Q: using

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Q: 2. In 00, AE is tangent to 00 at E, mZBCF = 112 and mBE:mDE = 3:7. Find: (а) тBЕ (b) mZA E A В C (c)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Consider V-x² + 4x +5 dx. Using trigonometric substitution, what is the integral form in terms of 0…

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Q: %3D 20 24 tan 24 through solve this egni: Hint :oU=KL +2 =0 மு 3K²=Par ET %3D 2.

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Q: X sin²= cos7 zcos'dx ·COS 2

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Q: 7 Jlgull sin(2) = e-e- 2i eiz-e-iz 2 et +e-iz 2i e -e-i: 2i

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Q: Determine whether y = e', y, = sin2t, ya= cos2t make up a fundamental set of solutions by finding…

A: The Wronskian matrix is constructed using y1 , y2 , y3 and their derivatives. If the determinant of…

Q: u(x,0) = x – x², u(0, t) = u(1,t) = 0, t>0, %3D - %3D Solve the following IBVP: Ut(x,0) = sin(27T),…

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Q: Use laplace trasfarng fo Solve dt² 2e cosi2t +e Sin at

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Q: Show that d?y dY + cot o- +a(@ + 1)Y = 0, 0 < 6 < T, do is transformed into Legendre's equation by…

A: Given:

Q: pe 19.27. F four equidistant values u_1, Uo, U1, and uz are given and a value u, is Enterpolated by…

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Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

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Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

Q: z2 = 2(cos7pi/12+isin7pi/12) what is (z2)^2 ? use de moivre law if needed

A: The given complex number is  z2 = 2(cos7pi/12+isin7pi/12)

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: a(t) = sech () tanh ()-ež. I t cle.

A: