Q4. Using Laplace Transforms determine the solution y(t),to the initial value problem following dy -4y dt = -7H(t-2), subject to the boundary condition y(o) = -4.

Q: b) Solve the given system of differential equation by laplace transformation dx = x - y dt dy — 5х —…

A:

Q: y', In(y) 1 y(e) = 1. x² In(x)

A:

Q: 1b) y" + 20y + 100y=p+qe, y (0) = 0, y (0)=0 where p= 100h, q=20h (av - 5), r = av Decompose the…

A:

Q: 2. The pdf of (X,Y) is 1 еxp TV3 fzy(x, y) ry+ 3 x<x < o, -00 < y < 0 Find the regression curve of Y…

A:

Q: O Consider the first order ODE dy + 3e-*y") dr – 3e Show that this is an exact equation, and hence,…

A:

Q: 7 Find the second linearly solution of the D.E x'y"+xy'-(x+2)y = 0, given that: y,(x) =

A:

Q: y" (t) + 2y' + y(t) = 8t²e-t.

A:

Q: The solution of the IVP t(t + 4)y + (t + 4) y= t, y(2) =2 exists in the interval

A: In the question it is asked to solve the initial value problem as shown below. t(t+4)y'+(t+4)y=t2…

Q: Suppose f(x) is continuous and positive for all æ except at x = 4, and Select the integrals that…

A: f(x) is continuous and positive for all x, except x=4 and ∫6∞f(x)dx converges.

Q: y" -y-2y 0. Assume that y, (t) = e and y2(t) = e" forma fundamental set of solutions. %3D (b) Let y3…

A:

Q: - - Find a particular solution Y(t) of y" — 2y" — y′ + 2y = e²t

A:

Q: (c) d²x dx dt dt Ix-0 +6+25x=e* with x(0)=0, dx dt Ix=0 = 0.

A:

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

A:

Q: Question (4): x'(t) = y(t) – 3x(t) + 3, y'(t) = 2x(t) – 4y(t) + 8 x(0) = 12, y(0) = 15

A:

Q: . Given the following system of equations, 2x1 +3r2+2r3 = 5 %3D 2.r1 +2r2 +3r3 = 12 %3D Ii+3r2 +3r3…

A:

Q: Use variation of parameters to find the particular solution to y'' + 5y' + 4y = 2e-34 Y(t) = […

A:

Q: Using the method of Laplace transformation, solve the following system of coupled ordinary…

A: The solution is given as

Q: Q2: (a): Solve (i) (x² D² – xD – 151I)y = 0 y(1) = 0.1, y'(1) = -4.5 (ii) 100 – 20 + d? N dN dt? dt

A:

Q: Find all functions that form a fundamental set of solutions for t2y" – 2ty' + 2y = 0. O y(t) = et O…

A: We have to solve given problem:

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

A:

Q: 2. Sketch the solid and set up an iterated triple integral in cylindrical coordinates for the volume…

A:

Q: consider the initial value problem (3,0227 y+25y=20,+7 410)=9.41(0)=0 1

A:

Q: Consider the IVP y"(t)-2y'(t) + 5y(t) = 0, y(0)=-1, y'(0)=3 (a) The characteristic equation of the…

A:

Q: 12:06 ■I 5G (8) If f(z) = √1+dt and g(y) = f (x)dx then find g"(#/3).

A: Thank you

Q: 8) (a). (8pts) Find a general solution to y" – 6y' + 9y = t-³e³3t by using variation of parameter…

A:

Q: Consider the equation y" y' - 2y = 0. Assume that y₁ (t) = e' and y₂(1) (b) Let Y3 (1) Y4 (t) = y₁…

A:

Q: Consider the equation y' – y – 2y = 0. Assume that y, (t) = e* and y, (1) = e2 form a fundamental…

A:

Q: Q5) (a) Solve by using Laplace transform the partial differential equation 8², =9. y(0,t)= 0, y(2,t)…

A:

Q: Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1-…

A: The differential equation dydx+y2x=x contains the highest derivativedydx which is of first order.…