math

Can someone please help?

Solve the differential equation

dy/dx = 6xy
with the condition y(0) = 40

Find the solution to the equation y= ______

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  1. This equation is separable, so
    dy/dx = 6xy
    dy/y = 6xdx
    Integrate both sides,
    log(y)=3x²+C1
    y=Ce3x²
    y(0)=40 -> C=40
    therefore
    y=40e3x²

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