Falak Kinney
2021-09-14
Answered

Use the method of Laplace transformation to solve initial value problem.

$\frac{dx}{dt}=x-2y,x\left(0\right)=-1,y\left(0\right)=2$

$\frac{dy}{dt}=5x-y$

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unessodopunsep

Answered 2021-09-15
Author has **105** answers

We know in Laplace transformation

Now Given IVP is

Taking laplace transformation on both the equation and both the side

From (1)

From (2)

Taking inverse laplace transformation both the side . We get

asked 2021-09-17

Find the solution of the integral equation f(t) using Laplace transforms

$f\left(t\right)=36t+5{\int}_{0}^{t}f(t-u)\mathrm{sin}\left(5u\right)du$

asked 2021-02-21

Find the Laplace transforms of the following time functions.

Solve problem 1(a) and 1 (b) using the Laplace transform definition i.e. integration. For problem 1(c) and 1(d) you can use the Laplace Transform Tables.

a)$f(t)=1+2t$
b)$f(t)=\mathrm{sin}\omega t\text{Hint: Use Euler\u2019s relationship,}\mathrm{sin}\omega t=\frac{{e}^{(}j\omega t)-{e}^{(}-j\omega t)}{2j}$

c)$f(t)=\mathrm{sin}(2t)+2\mathrm{cos}(2t)+{e}^{-t}\mathrm{sin}(2t)$

Solve problem 1(a) and 1 (b) using the Laplace transform definition i.e. integration. For problem 1(c) and 1(d) you can use the Laplace Transform Tables.

a)

c)

asked 2021-09-10

Find the Laplace transform

asked 2021-09-15

Find the Laplace transform by the method of definition.

$f\left(t\right)={e}^{\frac{t}{5}}$

asked 2021-08-21

asked 2022-01-16

Solve the Homogenous Differential Equations.

$(x-y\mathrm{ln}y+y\mathrm{ln}x)dx+x(\mathrm{ln}y-\mathrm{ln}x)dy=0$

asked 2022-04-30

I'm supposed to solve this using Laplace Transformations.