Solve the differential equation $x^2 \frac{∂u}{∂x}+y^2 \frac{∂u}{∂y}=u $ using the method of separation of variables if $u(0,y) = e^{\frac{2}{y}} $.

Question

TuteeHUB · Accepted Answer

$e^{\frac{3}{x}} e^{\frac{2}{y}} $

TuteeHUB · Answer

$e^{\frac{-3}{y}} e^{\frac{2}{x}} $

TuteeHUB · Answer

$e^{\frac{3}{y}} e^{\frac{2}{x}} $

TuteeHUB · Answer

$e^{\frac{-3}{x}} e^{\frac{2}{y}} $

TuteeHUB · Answer

$e^{\frac{3}{x}} e^{\frac{2}{y}} $

1.	Solve the differential equation \(x^2 \frac{∂u}{∂x}+y^2 \frac{∂u}{∂y}=u \) using the method of separation of variables if \(u(0,y) = e^{\frac{2}{y}} \).
A.	\(e^{\frac{-3}{y}} e^{\frac{2}{x}} \)
B.	\(e^{\frac{3}{y}} e^{\frac{2}{x}} \)
C.	\(e^{\frac{-3}{x}} e^{\frac{2}{y}} \)
D.	\(e^{\frac{3}{x}} e^{\frac{2}{y}} \)
Answer» D. \(e^{\frac{3}{x}} e^{\frac{2}{y}} \)

Solve the differential equation \(x^2 \frac{∂u}{∂x}+y^2 \frac{∂u}{∂y}=u \) using the method of separation of variables if \(u(0,y) = e^{\frac{2}{y}} \).