`dy/dx = 10x^4-2x^3` Use integration to find a general solution to the differential equation above.

Saturday, March 22, 2014

$\displaystyle\frac{{\left.{d}{y}}}{{\left.{d}{x}}}={10}{{x}}^{{4}}-{2}{{x}}^{{3}}$ Use integration to find a general solution to the differential equation above.

In order to use integration to solve this differential equation, multiply both sides of the equation by dx:

$\displaystyle{\left.{d}{y}\right.}={\left({10}{{x}}^{{4}}-{2}{{x}}^{{3}}\right)}{\left.{d}{x}\right.}$ .

Now we can integrate both sides, using the formula for the antiderivative of the power function: $\displaystyle\int{{x}}^{{n}}=\frac{{{x}}^{{{n}+{1}}}}{{{n}+{1}}}$

$\displaystyle{y}={10}\frac{{{x}}^{{5}}}{{5}}-{2}\frac{{{x}}^{{4}}}{{4}}+{C}$

Here, C is a constant. Since we are looking for a general solution of the equation which contains the first derivative, the solution has to include one arbitrary constant.

Simplifying the right side, we get

$\displaystyle{y}{\left({x}\right)}={2}{{x}}^{{5}}-\frac{{{x}}^{{4}}}{{2}}+{C}$ . This is the answer.

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Saturday, March 22, 2014

$\displaystyle\frac{{\left.{d}{y}}}{{\left.{d}{x}}}={10}{{x}}^{{4}}-{2}{{x}}^{{3}}$ Use integration to find a general solution to the differential equation above.

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Saturday, March 22, 2014

Use integration to find a general solution to the differential equation above.

No comments:

Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle\frac{{\left.{d}{y}}}{{\left.{d}{x}}}={10}{{x}}^{{4}}-{2}{{x}}^{{3}}$ Use integration to find a general solution to the differential equation above.

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?