Question

How do you solve this differential equation dydx=−xy when y=3 and x=4 ?

Answer 1

★Heya★

dy/y = -dx/x

integrating both sides.

ln ( y ) = - ln ( x ) + c

where c is called constant of integration.

ln ( 3 ) = - ln ( 4 ) + c

c = ln ( 12 )

$y = e {}^{ - ln(x) + ln(12)} \\ \\ y = e {}^{ln(12 \div x)}$