What is the solution for (dy)/(dx)=3xcos(x^2) ?

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

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(dy)/(dx)=3xcos(x^2)

\frac{d y}{d x} = 3 x cos (x^{2})

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

Solution steps

\frac{d y}{d x} = 3 x cos (x^{2})

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 3 x cos (x^{2})

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

then

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

y = \int 3 x cos (x^{2}) d x

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

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

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