Rivka Thorpe
2021-09-09
Answered

Find the length of the curve. $r\left(t\right)=<8t,{t}^{2},\frac{1}{12}{t}^{3}>,0\le t\le 1$

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Demi-Leigh Barrera

Answered 2021-09-10
Author has **97** answers

The curve will be

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Find

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Solve differential equation

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

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Solving separable ODEs

$\frac{dx}{dt}=f\left(x\right)g\left(t\right)$ with $x\left(0\right)={x}_{0}$

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Can 2 different ODE's have the same set of solutions?

If I have two differents linear ODE's:

${x}^{\text{'}\text{'}}+p\left(t\right){x}^{\text{'}}+q\left(t\right)x=f\left(t\right).\phantom{\rule{1em}{0ex}}p,q\in C(I,\mathrm{\infty}).$

${x}^{\text{'}\text{'}}+j\left(t\right){x}^{\text{'}}+g\left(t\right)x=h\left(t\right).\phantom{\rule{1em}{0ex}}j,g\in C(I,\mathrm{\infty}).$

Coul they have exactly the same set of solutions?

And if we have two different non-linear ODE's could they?

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Help needed solving logistic differential equation with initial conditions

$\frac{dP}{dt}=P(10-2P)$

with initial conditions of$P\left(0\right)=1.$

with initial conditions of

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Solution to ${x}^{\prime}=x\mathrm{sin}\left(\frac{\pi}{x}\right)$ is unique

I want to prove that the only solution to the ODE

${x}^{\prime}=\{\begin{array}{l}x\mathrm{sin}(\frac{\pi}{x})\text{if}x\ne 0\\ 0\text{else}\end{array}$

I want to prove that the only solution to the ODE

asked 2022-04-08

Understanding how to apply dominant balance method

I have the differential equation

$\u03f5y{}^{\u2033}-{x}^{2}{y}^{\prime}-y=0$

I have the differential equation