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

解

\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}

解答ステップ

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

代用

\frac{d y}{d x}

と

y^{'} (x)

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

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

であれば

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}