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

The solution for (dy)/(dx)=x(4x+5)^{1/3} is y= 1/16 (3/7 (4x+5)^{7/3}-15/4 (4x+5)^{4/3})+c_{1}

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

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

y = \frac{1}{16} (\frac{3}{7} (4 x + 5)^{\frac{7}{3}} - \frac{15}{4} (4 x + 5)^{\frac{4}{3}}) + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

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

\int x (4 x + 5)^{\frac{1}{3}} d x = \frac{1}{16} (\frac{3}{7} (4 x + 5)^{\frac{7}{3}} - \frac{15}{4} (4 x + 5)^{\frac{4}{3}}) + c_{1}

y = \frac{1}{16} (\frac{3}{7} (4 x + 5)^{\frac{7}{3}} - \frac{15}{4} (4 x + 5)^{\frac{4}{3}}) + c_{1}

f (x) = 2 x - x^{2}

\frac{d}{d x} (ln (x^{\frac{1}{x}}))

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What is the solution for (dy)/(dx)=x(4x+5)^{1/3} ?
The solution for (dy)/(dx)=x(4x+5)^{1/3} is y= 1/16 (3/7 (4x+5)^{7/3}-15/4 (4x+5)^{4/3})+c_{1}