13. Solve the initial-value problem dY dt -4 where the initial condition Yo is: (a) Yo = (1,0) (1) Y 2-3 Y, Y(0) Yo, (b) Yo (2, 1) = = (c) Yo (-1, -2)

Q: 7. Solve the initial value problem: 4y" – 4y – 3y = 0, y(0) = 1, y(0) = 5

A: Given : The differential equation is : 4y''-4y'-3y=0 y(0)=1  and  y'(0)=5

Q: GSolve the system 5 -6 dx x dt 10 with the initial value -11 x (0) 18 -3 x(t) =

A:

Q: Given Y = c1eλ1tx1 + c2eλ2tx2 +· · ·+cneλntxn is the solution to the initial value problem: Y = AY,…

A: Given that Y=c1eλ1tx1+c2eλ2tx2+.....+cneλntxn is the solution of the initial value problem Y'=AY,…

Q: A form of a particular solution to = 2x + 3y-7 dt = -x - 2y +5 is dt O (a b)" O (7, 5)" O (2, y)" O…

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Q: Problem #1: Solve the following initial value problem. -2y₁ - y2 y/₂2 бу1 — 732 Y = = y₁(0) = 5,…

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Q: 3 [₁³e- t³e-2t dt

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Q: Compute. (a) ds/dp if s = 3( p2 + 5p + 1)10 (b) d/dt (at2 + St-1 + S2)

A: (a) We have given s=3p2+5p+110. To find dsdp we have to differentiate s=3p2+5p+110 with respect to…

Q: 5. Find the linearization, L (x) f (a) + f' (a) (x – . a) of the given function "f" at "a". %3D - f…

A:

Q: 1. d²y dt2 dy + 6- +8y=2e-3t dt 2. d²y dy +4 dt² dt +13y = e-t 3. d²y dy +7 +10y=e-2t dt2 dt

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Q: Solve the following initial value problem Ans: r'(1)=(2r sin (2+²), r sint, ), r(0)= (1. 2, + 2 ) dt…

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Q: (D³ - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e²"+2e=x B y = (-1+ 2x)e-2r+e2r C y…

A: Given differential equation is (D3-3D-2)y = 0 with x=0,y=0,y'=9,y''=0.

Q: What is the solution to the initial – value problem : y" = x³ – 1 with y(0) = 8 and y'(0) = 0 ? y =…

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Q: Question 4: Consider the initial value problem aj + by + cy = f(t), y(0) = yo, (0) = y%, t> 0.…

A: Consider the given initial value problem.

Q: The differential equation y' = Vx+y+1–1 has the solution:

A: We need to solve the differential equation given by y'=x+y+1-1 The solution is given below.

Q: 3. (UD-1) Solve the following initial value problems using auxiliary equations: (a) y" + 6y' - 16y =…

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: The differential equation –y" = f(t), y(2) = 0. y(5) = 0 discretized with step-size h = has the…

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Q: (17) = ² × ( ¹²7 ) = ² × x=(²7)e²+(²1) ²² = ₁₁ (²₁) e² + c₂l(¹) te² + (1) e¹ dx dt dy dt O 2x + y -X…

A: The differential equations are:And,To Do:We have to solve the system.

Q: 2) Solve the given initial problem. ; y(0) = 2, y'(0) = -1 ; y(0) = 0, y'(0)=2 ; y(-1) = 2, y'(-1) =…

A: Since you have asked multiple subpart,as per our guidelines we are supposed to answer only first 3…

Q: Q1: A chemical process having two input variables and one output variable. If the response of the…

A: I/p variables : 2 O/p variables : 1 Step change in both cases : 2

Q: Compute the x(1)and x(4) for the function x(t) that satisfies the initial problem x"(t) + 2x(t) +…

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Q: ind the longes PtaV + (In(z- 2) )y = 0. y(3) = 1 and y(3) = 0

A:

Q: 9. Find the particular solution for each initial value problem. a) (2x + 3)y = where y(0) = 1 dx b)…

A: Particular solution:         The solution obtained by giving particular values to independent…

Q: 15. y = x³e*

A:

Q: olve the initial-value problem (IVP) below: da dt = 1 1 -5 -3 x, x(0) =

A: x'=1-51-3x, x0=11 which is of the form x'=Ax where A=1-51-3

Q: Solve the given initial problem. a) 9y"-12y'+4y = 0 ; y(0) = 2, y'(0) = -1

A: (a). From the given problem: 9y''-12y'+4y=0 So, we can also write as: 9D2-12D+4y=0 The auxiliary…

Q: . Let y (r) be the solution of the initial value problem y(4) - /" +2y +2y 0 y (0) = a, (0) = B, "…

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Q: Solve the IVP dx dt x(t) = -12 0] 1]* 118 -24 0J - x, x(0) = 1 -18

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Q: Define fct) = {est + e + cast if t 1/2 t>"/2 solve y(3) - 2 y(2) + ý' - 2y = f(t) y (0) = 1, y'(0) =…

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Q: 21. If F(x)= [ VP +1 dr, then F'(2) = %3D (A) -3 (В) -2 (C) 2 (D) 3 (E) 18

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Q: Consider the following initial value problem: Edit y" + 8y' + 15y = d(t – 5) + u10(t); y(0) = 0,…

A: We will find out the required solution.

Q: 6. Determine the output y(n) using the DTFT and IDTFT if x(n) = (0.5) "u(n) and 1, h(n) = {2, 0, n =…

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Q: This is the solution of y" + 4y' + 3y = 8 (t – 2) , y (0) = 0, y' (0) = 0 O y = [e-t-2) –e-8(t-2)] U…

A: