PEEWSRIGWETRYqx
2021-12-21
Answered

Find the general solution of the given differential equation.

$x}^{2}{y}^{\prime}+x(x+7)y={e}^{x$

$y=$

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enlacamig

Answered 2021-12-22
Author has **30** answers

Consider the differential equation

On rewriting it, we get

Standard form of the linear differential equation

Clearly equation (1) is in the standard form

Compare the differential equation (1) with standard orm, and identity

The dunctions

The integrating facrote is

Multiply the standart form, with the integrating factor

Hence the general solution of the given differential equation is

ol3i4c5s4hr

Answered 2021-12-23
Author has **48** answers

answer
Part 1 $\frac{1}{2{x}^{2}}{e}^{x}+C{x}^{-2}{e}^{-x}$

Part 2$(0,\mathrm{\infty})$

Part 3$C{x}^{-2}{e}^{-x}$

Part 2

Part 3

RizerMix

Answered 2021-12-29
Author has **438** answers

Thank you!!!!!!!

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Differentiate.

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find the Laplace transform by the method of the unit step function

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If we consider the equation

$(1-{x}^{2})\frac{{d}^{2}y}{{dx}^{2}}-2x\frac{dy}{dx}+2y=0,\text{}-1x1$

how can we find the explicit solution, what should be the method for solution?

how can we find the explicit solution, what should be the method for solution?

asked 2022-01-22

Quickly! Need help

Solve differential equation, subject to the given initial condition.

$x\frac{dy}{dx}+(1+x)y=3;\text{}\text{}y\left(4\right)=50$

Solve differential equation, subject to the given initial condition.

asked 2021-10-02

Find the general solution of the given differential equation.

$y-2y-3y=-3te-t-2y-3y=-3te-t$

asked 2022-06-16

I am familiar with first-order differential equations and how to solve them, but only for the case when there is a single unknown function.

For the following case there are two unknown functions and I'm struggling to determine where to even begin. The two equations:

$\begin{array}{}\text{(1)}& {f}^{\prime}(t)=-Af(t)+Bg(t)\end{array}$

$\begin{array}{}\text{(2)}& {g}^{\prime}(t)=-Bg(t)+Af(t)\end{array}$

Where f and g are functions of the variable t, and A & B are constants. The initial conditions are: $f(0)=0$ and $g(0)=1$.

I already have knowledge of the answer for f(t), which is:

$\begin{array}{}\text{(3)}& f(t)=\frac{B}{A+B}(1-{e}^{-(A+B)t})\end{array}$

I would really like to understand how to tackle questions of this type: where there are two unknown functions. I would attempt to show my working out but I don't know where to start.

Therefore, I would like to ask if anyone could please provide a hint or suggestion for me, something which I can work off. If necessary, I will update my post with original working. Thank you for your time.

For the following case there are two unknown functions and I'm struggling to determine where to even begin. The two equations:

$\begin{array}{}\text{(1)}& {f}^{\prime}(t)=-Af(t)+Bg(t)\end{array}$

$\begin{array}{}\text{(2)}& {g}^{\prime}(t)=-Bg(t)+Af(t)\end{array}$

Where f and g are functions of the variable t, and A & B are constants. The initial conditions are: $f(0)=0$ and $g(0)=1$.

I already have knowledge of the answer for f(t), which is:

$\begin{array}{}\text{(3)}& f(t)=\frac{B}{A+B}(1-{e}^{-(A+B)t})\end{array}$

I would really like to understand how to tackle questions of this type: where there are two unknown functions. I would attempt to show my working out but I don't know where to start.

Therefore, I would like to ask if anyone could please provide a hint or suggestion for me, something which I can work off. If necessary, I will update my post with original working. Thank you for your time.

asked 2021-09-14

The Laplace transform $L\left\{{e}^{-{t}^{2}}\right\}$ exists, but without finding it solve the initial-value problem $y{}^{\u2033}+y={e}^{-{t}^{2}},y\left(0\right)=0,{y}^{\prime}\left(0\right)=0$