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ZanzabumX [31]
3 years ago
10

Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

Mathematics
1 answer:
Mama L [17]3 years ago
6 0

Multiplying both sides by y^2 gives

xy^2\dfrac{\mathrm dy}{\mathrm dx}+y^3=1

so that substituting v=y^3 and hence \frac{\mathrm dv}{\mathrm dv}=3y^2\frac{\mathrm dy}{\mathrm dx} gives the linear ODE,

\dfrac x3\dfrac{\mathrm dv}{\mathrm dx}+v=1

Now multiply both sides by 3x^2 to get

x^3\dfrac{\mathrm dv}{\mathrm dx}+3x^2v=3x^2

so that the left side condenses into the derivative of a product.

\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2

Integrate both sides, then solve for v, then for y:

x^3v=\displaystyle\int3x^2\,\mathrm dx

x^3v=x^3+C

v=1+\dfrac C{x^3}

y^3=1+\dfrac C{x^3}

\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}

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I assume you mean x squared in the first equation

Because both are equal to y, they are equal to each other so x + 5 = x^2 +3
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Then factorise it to (x-2)(x+1) = 0
And solve both parts separately

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1 year ago
a person walks 80 feet in 40 seconds. what equation represents this relationship. how many feet will the person walk in 10 secon
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Answer:

20 feet

Step-by-step explanation:

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\frac{x}{10} = \frac{20}{10}

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soldi70 [24.7K]

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