Tahmid Knox
2021-02-12
Answered

On solution of the differetial equation ${y}^{\u2033}+{y}^{\prime}=0$ is $y={e}^{-x}$ . Use Reduction of Order to find a second linearly independent solution.

You can still ask an expert for help

bahaistag

Answered 2021-02-13
Author has **101** answers

In such problems ie second order linear differential equations when we are given one solution,

Compute:

Substitute

Let

Substitute

Integrating we get

Get second linearly independent solution by substituting v in expression for

Hence second linearly independent solution is c

asked 2022-01-02

Non-Homogeneous Linear Differential Equation (The Method of Undetermined Coefficients).

Solve the equation$(D+1)y=\mathrm{sin}x$

Solve the equation

asked 2021-02-02

Solve the following differential equations using the Laplace transform and the unit step function

$y"+4y=g(t)$

$y(0)=-1$

${y}^{\prime}(0)=0,\text{where}g(t)=\{\begin{array}{ll}t& ,t\le 2\\ 5& ,t2\end{array}$

$y"-y=g(t)$

$y(0)=1$

${y}^{\prime}(0)=2,\text{where}g(t)=\{\begin{array}{ll}1& ,t\le 3\\ t& ,t3\end{array}$

asked 2021-09-17

use laplace transform to solve the following initial value problem:

asked 2021-12-31

Solve the differential equations $(t-1)3d\frac{s}{dt}+4(t-1)2s=t+1,t>1$

asked 2021-02-21

Solve differential equation${y}^{\prime}+3{x}^{2}y=\mathrm{sin}\left(x\right){e}^{-{x}^{3}},\text{}y\left(0\right)=1$

asked 2021-12-09

Using the Laplace Transform Table in the textbook and Laplace Transform Properties,find the (unilateral) Laplace Transforms of the following functions:

$u\left(t\right)-u(t-1)$

asked 2022-04-14

Laplace transform of $f\left(t\right)=t{e}^{-t}\mathrm{sin}\left(2t\right)$