What is the solution for (dy)/(dx)=x^{1/4}+x^{-3/5} ?

The solution for (dy)/(dx)=x^{1/4}+x^{-3/5} is y= 4/5 x^{5/4}+5/2 x^{2/5}+c_{1}

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(dy)/(dx)=x^{1/4}+x^{-3/5}

\frac{d y}{d x} = x^{\frac{1}{4}} + x^{- \frac{3}{5}}

y = \frac{4}{5} x^{\frac{5}{4}} + \frac{5}{2} x^{\frac{2}{5}} + c_{1}

Solution steps

\frac{d y}{d x} = x^{\frac{1}{4}} + x^{- \frac{3}{5}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x^{\frac{1}{4}} + x^{- \frac{3}{5}}

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

then

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

y = \int x^{\frac{1}{4}} + x^{- \frac{3}{5}} d x

\int x^{\frac{1}{4}} + x^{- \frac{3}{5}} d x = \frac{4}{5} x^{\frac{5}{4}} + \frac{5}{2} x^{\frac{2}{5}} + c_{1}

y = \frac{4}{5} x^{\frac{5}{4}} + \frac{5}{2} x^{\frac{2}{5}} + c_{1}

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What is the solution for (dy)/(dx)=x^{1/4}+x^{-3/5} ?
The solution for (dy)/(dx)=x^{1/4}+x^{-3/5} is y= 4/5 x^{5/4}+5/2 x^{2/5}+c_{1}