Linear equations of second order with constant coefficients. Find all solutions on {left(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

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Linear equations of second order with constant coefficients. Find all solutions on {left(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

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asked 2021-02-21

Linear equations of second order with constant coefficients.
Find all solutions on
\(\displaystyle{\left(-\infty,+\infty\right)}.{y}\text{}-{2}{y}'+{5}{y}={0}\)

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Linear equations of second order with constant coefficients. Find all solutions on \(\displaystyle{\left(-\infty,+\infty\right)}.{y}\text{}+{4}{y}={0}\)

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asked 2021-02-12

\(y=3e^{3x}\) is a solution of a second order linear homogeneous differential equation with constant coefficients. The equation is:
(a) \(y''-(3+a)y'+3ay=0\), a any real number.
(b) \(y''+y'-6y=0\)
(c) \(y''+3y'=0\)
(d) \(y''+(3-a)y'+3ay=0\), a any real number.
(e) Cannot be determined.

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asked 2021-03-08

Linear equations of first order.
Solve the initial-value problem on the specified interval \(\displaystyle{y}'-{3}{y}={e}^{{{2}{x}}}{o}{n}{\left(-\infty,+\infty\right)},\ \text{with}\ {y}={0}\ \text{when}\ {x}={0}\).

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asked 2021-06-06

Consider the differential equation for a function f(t),
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c)Find a particular solution with f(0)=0
2. Find the particular solutions to the differential equations with initial conditions:
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b)\(\frac{dy}{dx}=e^{4x-y}\) with y(0)=0

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asked 2020-12-07

Solve the second order linear differential equation using method of undetermined coefficients
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Using the existence and uniqueness theorem for second order linear ordinary differential equations, find the largest interval in which the solution to the initial value is certain to exist.
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Solve the following IVP for the second order linear equations
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asked 2020-11-09

Let \(y_1\) and \(y_2\) be solution of a second order homogeneous linear differential equation \(y''+p(x)y'+q(x)=0\), in R. Suppose that \(y_1(x)+y_2(x)=e^{-x}\),
\(W[y_1(x),y_2(x)]=e^x\), where \(W[y_1,y_2]\) is the Wro
ian of \(y_1\) and \(y_2\).
Find p(x), q(x) and the general form of \(y_1\) and \(y_2\).

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asked 2021-02-12

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

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Answer 1

The characteristic equation is given by
\({r}^{2}+{2}{r}+{1}={0}\)
and has the roots \(r_1=11 and r_2=1\).
The general solution is given by
\({y}={e}^{x}{\left({c}_{{1}}+{c}_{{2}}{x}\right)}\), where c_1 and c_2 are arbitracy constant.

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Linear equations of second order with constant coefficients. Find all solutions on {left(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

Linear equations of second order with constant coefficients. Find all solutions on {left(-infty,+inftyright)}.{y}text{}+{2}{y}'+{y}={0}

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