Wierzycaz
2020-12-05
Answered

Solve $y=-2x\left(y\right)$

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Khribechy

Answered 2020-12-06
Author has **100** answers

Given that y''=−2x(y)

where

where

Hence the solution of the given Differential equations is

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Determine whether the following differential equations are exact or not exact. if exact, solve for the general solution

$(x+2y)dx-(2x+y)dy=0$

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Solve differential equation${y}^{\prime}+4y=128x$

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Finding eigenvalues by inspection?

I need to solve the following problem,

In this problem, the eigenvalues of the coefficient matrix can be found by inspection and factoring. Apply the eigenvalue method to find a general solution of the system.

$x}_{1}^{{}^{\prime}}=2{x}_{1}+{x}_{2}-{x}_{3$

$x}_{2}^{{}^{\prime}}=-4{x}_{1}-3{x}_{2}-{x}_{3$

$x}_{3}^{{}^{\prime}}=4{x}_{1}+4{x}_{2}+2{x}_{3$

Now I know how to find the eigenvalues by using the fact that$|A-\lambda I|=0$ , but how would I do it by inspection? Inspection is easy for matrices that have the sum of their rows adding up to the same value, but this coefficient matrix doesn't have that property.

EDIT: Originally I didn't understand what inspection meant either. After googling it this is what I found. Imagine you have the matrix,$$A=(\begin{array}{ccc}2& -1& -1\\ -1& 2& -1\\ -1& -1& 2\end{array})$$

By noticing (or inspecting) that each row sums up to the same value, which is 0, we can easily see that [1, 1, 1] is an eigenvector with the associated eigenvalue of 0.

I need to solve the following problem,

In this problem, the eigenvalues of the coefficient matrix can be found by inspection and factoring. Apply the eigenvalue method to find a general solution of the system.

Now I know how to find the eigenvalues by using the fact that

EDIT: Originally I didn't understand what inspection meant either. After googling it this is what I found. Imagine you have the matrix,

By noticing (or inspecting) that each row sums up to the same value, which is 0, we can easily see that [1, 1, 1] is an eigenvector with the associated eigenvalue of 0.

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Please solve the 2nd order differential equation by (PLEASE FOLLOW GIVEN METHOD) LAPLACE TRANSFORMATION

ALSO, USE PARTIAL FRACTION WHEN YOU ARRIVE

Problem 2 Solve the differential equation

and

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Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by

$F\left(s\right)={\int}_{0}^{\mathrm{\infty}}{e}^{-st}f\left(t\right)dt$

where we assume s is a positive real number. For example, to find the Laplace transform of$f\left(t\right)={e}^{-t}$ , the following improper integral is evaluated using integration by parts:

$F\left(s\right)={\int}_{0}^{\mathrm{\infty}}{e}^{-st}{e}^{-t}dt={\int}_{0}^{\mathrm{\infty}}{e}^{-(s+1)t}dt=\frac{1}{s+1}$

Verify the following Laplace transforms, where u is a real number.

$f\left(t\right)=\mathrm{cos}at\to F\left(s\right)=\frac{s}{{s}^{2}+{a}^{2}}$

where we assume s is a positive real number. For example, to find the Laplace transform of

Verify the following Laplace transforms, where u is a real number.

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Solve differential equation$x{y}^{\prime}+[(2x+1)/(x+1)]y=x-1$

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Linear approximation at $x=0$ to $\mathrm{sin}(6x)$