What is the solution for (dy)/(dx)= x/(sqrt(x^2+64)) ?

The solution for (dy)/(dx)= x/(sqrt(x^2+64)) is y=sqrt(x^2+64)+c_{1}

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(dy)/(dx)= x/(sqrt(x^2+64))

\frac{d y}{d x} = \frac{x}{x ^{2} + 64}

y = x^{2} + 64 + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x}{x ^{2} + 64}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{x}{x ^{2} + 64}

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

then

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

y = \int \frac{x}{x ^{2} + 64} d x

\int \frac{x}{x ^{2} + 64} d x = x^{2} + 64 + c_{1}

y = x^{2} + 64 + c_{1}

n = 1 \sum \infty n! (2 x - 1)^{n}

\frac{d x}{d t} = - 8

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

\int (6 x y + 4 x) d y

(- 5, - 8), (9, - 8)

What is the solution for (dy)/(dx)= x/(sqrt(x^2+64)) ?
The solution for (dy)/(dx)= x/(sqrt(x^2+64)) is y=sqrt(x^2+64)+c_{1}