What is the solution for (dy)/(dx)=sqrt(9+3x) ?

The solution for (dy)/(dx)=sqrt(9+3x) is y= 2/9 (9+3x)^{3/2}+c_{1}

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(dy)/(dx)=sqrt(9+3x)

\frac{d y}{d x} = 9 + 3 x

y = \frac{2}{9} (9 + 3 x)^{\frac{3}{2}} + c_{1}

Solution steps

\frac{d y}{d x} = 9 + 3 x

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 9 + 3 x

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

then

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

y = \int 9 + 3 x d x

\int 9 + 3 x d x = \frac{2}{9} (9 + 3 x)^{\frac{3}{2}} + c_{1}

y = \frac{2}{9} (9 + 3 x)^{\frac{3}{2}} + c_{1}

\frac{d}{d y} (arcsin (y))

\int x n x d x

sin (θ) + cos (θ) θ

\int \frac{x ^{2}}{1 - x} d x

\int \frac{4 u}{16 u ^{2} + 7} d u

What is the solution for (dy)/(dx)=sqrt(9+3x) ?
The solution for (dy)/(dx)=sqrt(9+3x) is y= 2/9 (9+3x)^{3/2}+c_{1}