Test the statement "The differential equation dy/dx = (x5 + y5) / (x5- y5) is homogeneous"
Answer & explanation
Correct answer: option 1
Let dy/dx = (x5 + y5) / (x5- y5) = f(x,y)
⇒f(tx,ty) = {(tx)5 + (ty)5)} / {(tx)5- (ty)5}
⇒f(tx,ty) = t0 {f(x,y)}
Hence, given differential equation is homogeneous differential equation.