5. x = et, y = 2e-t

Q: 20.tvaluate :L[t cosh 14t] A, 3s? +19le s²+196 C. (5?-1967? (6?-196)? -s?+ 196 s?-196 B. D.…

A: Using property of Laplace transform

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Q: 3. 2t t dt ST-t

A: To integrate the given vector function. ∫te2t, t1-t,11-t2dt...(1)

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Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

Q: solve the intial value problem y'' + 6y' + 9 = 0 , y(0)=2 , y'(0)=-5

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A: We have to find integral

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A: We have to solve the given integration and find out which option is correct.

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Q: 4[8,(t-2) rect(r)dt

A: we have,  I=4∫020δ4t-2recttdt we know that  ∫t1t2xtδt-t0dt=xt0 ;   t1<t0<t20       ;…

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Q: 14. 2ste-ds + (s?e-t - t)dt = 0

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Q: -5-S"S, ((m-3)x²+m(m -! x- Yy)-4myx] dydx 2,3m

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A: Please ask only one question at a time.

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A: Given that, x=tt-1y=t2t2-1 Then we get,…

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Q: 11. (4+ t) dt 13. | – 5y) dy 15. (31² – 4t + 5) dt

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Q: If y = ee then y' – y" + e"y' is equal to

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Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: 9. If x2-xy + y2 = 3, find y' and y", %3D

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Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

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Q: .1//3 7earctan(y) dy + y? 3

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Q: 1. 2tds + s(2 + s²t)dt = 0

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

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Q: /1- 7y² dy

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Q: B) fometie w= xty+y2-23, x²ry*+2?=6

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 10 | (1-e-t/4) dt 0,

A: Given integral, ∫0101-e-t4 dt

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A: Given: y=lncschx+cothx

Q: 2+ Problem 3/ Evaluate z*dz along the line y=

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Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: 3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 10. 2ste tds +(s²e-t - t)dt = 0 C = s²t-te² + e²

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Q: If s = 4/t - 3, then %3D ds dt

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Q: لله √ √³ √ √² zysin(2² + y²) dz dy −

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Q: S(6 + 6y – y²) dy

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Q: dt | sec? 3 3.

A: Given: An integral ∫sec2t3dt Integral of sec2x is given by∫sec2x=tan x+C. Using the formula…

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: 31. *7/2 csc t cot t dt

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Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr

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Q: find the 2 first non-zero of the inihiall value problem terms of the solu h'on x² y" +Clt x)y'+…

A: We find the first two non zero terms of the solution of the given initial value problem by power…

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Q: 4.1+ ež - ) ež + (ež )y' = 0 ex + (ex )y' = 0

A: