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Question

Mathematics for Economy Question on Differential Equations

The solution of the differential equation
xy𝑑𝑥(x2+y2)𝑑y=0,y(0)=1xy 𝑑𝑥 − (x^2 + y^2) 𝑑y = 0, y(0) = 1 is

A

𝑦=exy𝑦= e^{\frac{x}{y}}

B

y2=ex2y2y^2= e^{\frac{x^2}{y^2}}

C

y2=exyy^2= e^{\frac{x}{y}}

D

y=ex2y2y= e^{\frac{x^2}{y^2}}

Answer

y2=ex2y2y^2= e^{\frac{x^2}{y^2}}

Explanation

Solution

The correct answer is (B): y=ex2y2y^= e^{\frac{x^2}{y^2}}