How do you find the general solution of the differential equation #dy/dx=x^(3/2)#?

Answer 1

Emma Aldridge

Solve for #dy#.

#dy = x^(3/2)dx#

Integrate both sides.

#int(dy) = int(x^(3/2))dx#

Use the rule #int(x^n)dx = (x^(n + 1))/(n + 1) + C# to solve.

#y = x^(5/2)/(5/2) + C#

#y = 2/5x^(5/2) + C#

Hopefully this helps!

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Answer 2

Charles Anctil

To find the general solution of the differential equation ( \frac{dy}{dx} = x^{3/2} ), you can integrate both sides with respect to ( x ):

[ \int \frac{dy}{dx} , dx = \int x^{3/2} , dx ]

Integrating ( x^{3/2} ) with respect to ( x ) gives:

[ \int x^{3/2} , dx = \frac{2}{5} x^{5/2} + C ]

Where ( C ) is the constant of integration.

Therefore, the general solution to the differential equation is:

[ y = \frac{2}{5} x^{5/2} + C ]

Where ( C ) is an arbitrary constant.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.