What is a solution to the differential equation $dy/dt=e^t/(4y)$ ?

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Answer 1 · 2016-09-16T18:16:03

$y = pm sqrt( 1/2 e^t + C)$

$dy/dt=e^t/(4y)$

we separate it

$4y dy/dt=e^t$

we integrate: $int ( 4y dy/dt=e^t) dt$

$implies int 4y dy =int e^t dt$

$implies 2 y^2 = e^t + C$

$y = pm sqrt( 1/2 e^t + C)$

What is a solution to the differential equation dy/dt=e^t/(4y)dy/dt=e^t/(4y)?