What is a solution to the differential equation $dy/dx=x^2y$ ?

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Answer 1 · 2016-08-02T03:23:23

$y=Ce^(x^3/3)$

First, separate the variables:

$dy/dx=x^2y" "=>" "dy/y=x^2dx$

Integrate both sides:

$intdy/y=intx^2dx" "=>" "ln(y)=x^3/3+C$

Solve for $y$ :

$y=e^(x^3/3+C)=e^(x^3/3)(e^C)=Ce^(x^3/3)$

What is a solution to the differential equation dy/dx=x^2ydy/dx=x^2y?