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Popular >

(dy)/(dx)=x^{3/2}

Solution

\frac{d y}{d x} = x^{\frac{3}{2}}

Solution

y = \frac{2}{5} x^{\frac{5}{2}} + c_{1}

Solution steps

\frac{d y}{d x} = x^{\frac{3}{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x^{\frac{3}{2}}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x^{\frac{3}{2}} d x

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}} + c_{1}

y = \frac{2}{5} x^{\frac{5}{2}} + c_{1}

Popular Examples

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x = y^{2}, x = 6 - 2 y^{2}

integral of (9xsqrt(1+2x^2))

\int (9 x 1 + 2 x^{2}) d x

limit as x approaches 0 of (x^2-x)/x

x \to 0 lim (\frac{x ^{2} - x}{x})

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=x^{3/2} ?
The solution for (dy)/(dx)=x^{3/2} is y= 2/5 x^{5/2}+c_{1}