Question

A solução particular da equação diferencial separável y' -2xy=0 com y (3)=e , é:

Answer 1

$y' -2xy=0\\\\ y' = 2xy\\\\ \frac{dy}{dx}= \frac{2x}{y}\\\\ \frac{1}{y} \;dy = 2x\; dx\\\\ \int \frac{1}{y} \;dy = \int 2x\; dx\\\\ ln(y)=x^2+C\\\\y=e^{x^2+C}\\y=C*e^{x^2}\\\\ \boxed{y(3)=e}\\\\e=C*e^{3^2}\\\\ e^{-8}=C\\\\ \boxed{\boxed{y(x)=e^{-8}*e^{x^2} = e^{x^2-8}}}$