d²f , df_ (a) +5- - + 6f =0, f(0)=1, f(0) =- 4 dt? dt

Q: How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.

A: Converting the equation in Laplace transform:…

Q: Solve the following problem using Laplace transforms.  utt = c2uxx − g, x > 0, t > 0,  u(0,t)=0, t…

A: We have following problems: utt=c2uxx-g, x>0,t>0 Taking Laplace both sides…

Q: find the laplace transform of the equation: f(t)= 2t^3 e^-4t

A:

Q: Use matrix to solve for X(s) and Y(s) in the equations below and find the laplace transform of X(s)…

A: To solve the given problem Simplify for X(s) and Y(s)  Using inverse laplace transformation solve…

Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: h(t)=t^2sin(3t) laplace transform

A: Given function is,                h(t) = t2 sin3t (.)  Some properties of Laplace transform :- (i)…

Q: Find the inverse Laplace transforms: Y(s)=(2s+3)/((s+5)^2+4)

A: 2e−5t(4cos(2t)−7sin(2t))​Explanation:

Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

A:

Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

A:

Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

A:

Q: Use Laplace transformations to solve the IVP y" – y' = 0 - y(0) = y'(0) = 1 Show the complete…

A: The detailed solution is given below Thank you

Q: Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D

A: Given the given equation is y"+9y=δt-π6sint,     y0=0,  y'0=0 Use the property of delta function.…

Q: 4. Solve the initial value problem: y" + 3y' – 10y = 0, y(0) = 1, y'(0) = 0 -

A:

Q: x^2y′′ + (3/2xy′ + [(1/36)x^2/3 − 7/144]y = 0 z = (1/2)x^1/3, w = yx^1/4 Solve it using the…

A: The transform method can be used to find the solution to the differential equation x^2y′′ + (3/2xy′…

Q: 2. f(t) = -7(e^3t)[sinh(2t)] A. -14 / (s^2 – 6s + 5) B. (-7s + 21) / (s^2 – 6s + 5) C. -14 / (s^2 -…

A:

Q: Find the inverse Laplace transforms of F(s)=(5s + 2)/(s^2+6s + 13)

A: to find the inverse Laplace of the function proceed as follows Fs=5s+2s2+6s+13 make the partial…

Q: -2sin4t Determine the Laplace transform of the equation f (x) = 2 e´ 10 A s²+4s+20 8 B s²+4s+ 20 20…

A:

Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

A:

Q: Use Laplace transforms to solve the IVP y''+1=0, y(0)=1, y'(0)=1

A:

Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

A:

Q: у"" + Зу" + Зу' %3D у У(0) 3D 7, у' (0) — -7, у" (0) — 11

A: We have to apply the Laplace transform method.

Q: find

A:

Q: 1. Find the Fourier transform of f(t) defined by: 0 t<0 e-6t t20 f(t A. (6- jw)/(36+ w^2) B. (6 +…

A: Fourier transform of the pice wise function