What is the solution for dy=x^2dx,y(0)=0 ?

The solution for dy=x^2dx,y(0)=0 is y=(x^3)/3+c_{1}

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dy=x^2dx,y(0)=0

d y = x^{2} d x, y (0) = 0

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

Solution steps

d y = x^{2} d x

Let

y

be the dependent variable. Divide by

d x

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

y = \int x^{2} d x

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

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

\int \frac{x}{1 - x ^{3}} d x

\int \frac{sin ( x )}{( 1 + cos ( x ) )} d x

\frac{1}{x + 8}

\int (tan^{2} (x) + 1) d x

f (x) = 9 sin (3 x)

What is the solution for dy=x^2dx,y(0)=0 ?
The solution for dy=x^2dx,y(0)=0 is y=(x^3)/3+c_{1}