Toronto Math Forum
MAT2442018F => MAT244Lectures & Home Assignments => Topic started by: Qinger Zhang on September 23, 2018, 04:50:56 PM

why (d^3y)/(dt^3) + t (dy)/(dt) +(cos^2(t))y = t^3 is linear? It doesn't have second derivative of dy dt, so it is not a linear equation.

A linear differential equation is in the form of $a_0(t)y^{(n)} + a_1(t)y^{(n1)}+ ... + a_n(t)y = g(t)$, and also $a_i(t)$ can be a constant function which is: $a_i(t) = C$.
In this case, $a_1(t) = 0$, so the second derivative $y^{''}$ disappears. However, it's still a linear differential equation.