Question

Applying Initial Conditions 7) Verify that y = cer is a solution, for any real c, of v' = 21y. Determine c so that y(0) = 2.

Answer 1

y = Ce^t^2 equation (1) Apply differentiation on both sides of eqn (1) wrt 't' d(y)/dt = d/dt (ce^t^2) dy/dt = C de^t^2/dt (C is constant) y^' = C e^t^2 d(t^2)/dt = C middot e^t^2 middot 2t y^' = y middot 2t implies y^' = 2ty (therefore from eqn (1)) y = Ce^t^2 therefore y = Ce^t^2 is a solution, for any real C, of y^' = 2ty. Y(0) = 2 implies C middot e^(0)^2 = 2 implies C middot e^0 = 2 implies C middot 1 = 2 C = 2