(b) Use the Laplace transform method to find the solution of d²y 6+9y= 4e", yo = 2, y1 = 0. dt dy %3D

Q: Q"+4Q'+4Q=2t Solve with Laplace transform

A: Using laplace transform to solve the problem.

Q: y" + 3y" + 3y = y y (0) = 7, y' (0) = -7, y" (0) = 11

A: We will use following Laplace transformation…

Q: у" +у%3D0.001t?, У (0) %3D 0, у'(0) %3D 1.5

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Q: x2y3-y=x+x2 find dy/dt

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Q: solve: y" - Hý + 4y = 40st; y(0)=2₁ y(0)=5 using Laplace transform

A: y''-4y'+4y=4cos 2t Taking Laplace transform on both…

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: Solve the equation using Laplace transform y" - 6y' +9y t²e³t, y(0) = 2, y'(0) = 6. =

A: Introduction: There are many different ways that are applied to solve an initial value problem. One…

Q: find the a general solution to dy/dt = {{-9,12},{6,-8}}y

A: (.)  Given ,            (.)  Consider a system of differential equation ,…

Q: (x' = x- 2y V = 5x – yi x(0) = -1, y(0) = 2. %3D %3D %3D %3D

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Q: Let F(x) = dt. Then %3D 25 (t + t10)15 F'(x) = %3D

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Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: Solve using the Laplace transform y' + 2y = 12 e3t , y(0) = 3

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Q: -- solve ÿt y-2y=5é'sint ,y (0)=1 and o)=o using Laplace transforms.

A: We have to find solution by Laplace transform Method.

Q: Use Laplace transform to solve the DE. d²y_3dy = 9 dx² dx where x=0, x=0 and dy=0 dx

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Q: 1 dt. 1+ vt Let G(x) Find G'(9).

A: Given that: G(x) = ∫2x211+tdt

Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: + y = ty dt

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Q: Draw the bifurcation diagram for dy/dt = y(a-y)

A: We can use concept of critical points in order to solve the given problem.

Q: Solve the IVP using Laplace Transform y" = y + 2y, y(0) = -2, y (0) = 3.

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Q: J(2t-3)-e-t²,3t i. 2t – dt 3 2vlnx dx . ii. X 2 iii. (2y-3]12 kdy.

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Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

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Q: Use Raplace Transform to Solue y?+3y'+2y=DUglt) O and %3D guen ylo) =0 y'l6)=1 %3D

A: Use Laplace table to solve this.

Q: y"+2ў-15y=0 усо)=1 y'(0)=-2

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Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

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Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: Use Laplace Transform to solue y' +zy y=4et %3D given ylo)"= 2 and y'lo). y'66)=-1 %3D

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Q: t2+1 = 0 dv Vt- dt V+1

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Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: Find dy/dx

A: Here we use fundamental theorem of calculus, in which to find the derivative of a definite integral…

Q: Solve by using Laplace Transform and explain the steps in brief d?x dx +2 +x= 3te dt? dt Given x(0)…

A: The given differential equation is: d2xdt2+2dxdt+x=3te-t  …1 Given: x0=4; x'0=2