7. When the given differential equation is Solved using Laplace transform Method, the equivalint subsidiary equaton with y (0) =1 and y'(0) =-2is. y"+ ay + y=tet 7. %3D (s?+ 2s +1) y (s) = a- %3D 2. b.(5?+$+1)y(s) = st- (Sti)?

Q: en differential equation by using an appropriate substitution. The DE is ho + (x + Vxy) dy = 0 %3D

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Q: y" -y + 2x t2 where: a (0) = a' (0) = 0 %3D y (0) = y (0) = 0 Find: L (y) L (y) 293 s+2 - OL (y) = 2...

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Q: Answer the following True or False: For any function f(x) that is differentiable at z = 9. f( – 9 + ...

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Q: ii) Show that lim - 1+22+33 +...+n' "]=1 1/n

A: Apply Cauchy Frist theorem on limit

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Q: Find the exact length of the curve. 1 y = -x° 4 x² -- In(x), 1<x< 4 | 2

A: Given curve, y=14x2-12lnx   ;  1≤x≤4  

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Q: dy A possible solution to the differential equation t dt (2) + 2y = 4t + 1 would be: y = # + 4t 1 3 ...

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Q: Tx?+y?)dx + 3xydy

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Q: If f(x)=3lnx​:   A. An estimate of f′(1) using the interval from 1 to 1.1 is_____. B. An estimate of...

A: Given:     f(x) = 3 ln x

Q: Find f'(a). 2t + 12 (t) t + 9 f'(a):

A: Given that: f(t)=2t+12t+9

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Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

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Q: 10. Sec -405 degrees 12. Cot -90 degrees 14. cos 360 degrees  16. sin -225 degrees

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Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32 ft/...

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

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Q: Find the approximations T, M and S, for n = 6 and 12. Then compute the corresponding errors ET, EM, ...

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Q: Find L{(t – 1) (2 – 5 sin 3t)}. 2 15 15 + s(s² +9) s2 (s² +9) 5s 30s s2 +9 (82–9)² 2 15 15 s2 (s² –9...

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. dx = 12+36

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Q: 5. ( arcsin(x – 1) dx

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Q: d'y Given the differential equation + y = e-6" sin(x) dx? Propose an appropriate particular solution...

A: follow the procedure given below.

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Q: If the Laplace Transform of F (t) = /t3 is 4s 2 what is the Laplace Transform of F (t) = e' Vt3? 4(s...

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Q: Differentiate each function with respect to x. 1. y = ((2x^3-1)^5+ 1)^3 2. y = ((-5x-3)^5 + 1)^2 3. ...

A: 1. y = ((2x3 -1)5 + 1)3 2. y = ((-5x-3)5 + 1)2 3. y = ((x3 -2)5 - 2)3 Repost the next parts.

Q: If f)=6X+12, hind the slopeof the secaut line between the values of X,= -5 and Xa = - 6- %3D

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Q: Find the exact length of the curve. 4 1 X = 1<y< 3 + 8 4y2"

A: we will find the exact length of the curve.

Q: 2 - = 3t y+ x' = 3et * (0) = y (0) = 0 OL (x) = 3s2 (s+1)(s–2)(s²+1) 3(s-1) OL (z) = 76+1) (28²+1) s...

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Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32 ft/...

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Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

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Q: I. The Derivatives: Perform long method. 1. v = Ja2 – y? 2. x = 3t2 - 2 Vt

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Q: Evaluate f (2x + 1) dx by two methods: (a) Expand (2.x +.1)' by the binomial theorem; (b) let u = 2x...

A: Given that ∫2x+13dxa. using binomial expantion2x+13=c302x3+c312x21+c322x112+c3313=8x3+34x2+32x+1=8x3...

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