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

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

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

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (x + 2)^{2}

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

then

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

y = \int (x + 2)^{2} d x

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

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

\frac{d}{d x} (arctan (\frac{y}{x}))

4 t \frac{d y}{d t} + y = t^{6}

x \to 0 lim (\frac{sin ( - 5 x )}{x})

\int x^{2} + cos (x) d x

2 π r

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