(3) The ODE y′=x−2yy+2x​ features several symmetries: It is rotational invariant and also homogeneous (of degree 1) (a)

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3 The Ode Y X 2yy 2x Features Several Symmetries It Is Rotational Invariant And Also Homogeneous Of Degree 1 A 1 (45.36 KiB) Viewed 26 times

(3) The ODE y′=x−2yy+2x​ features several symmetries: It is rotational invariant and also homogeneous (of degree 1) (a) Solve this ODE by switching to polar coordinates, as worked out in Tutorial 1. Show that the family of solutions is rotational invariant, i.e. rotating any given solution yields another solution. (b) Solve this ODE as a homogeneous ODE using the substitution u(x)=xy(x)​ from above and show that the family of solutions is invariant with respect to the scaling (x,y)↦(λx,λy).