### Author Topic: problem 6 in 1.3  (Read 925 times)

#### Qinger Zhang

• Jr. Member
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##### problem 6 in 1.3
« 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.

#### Wei Cui

• Full Member
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##### Re: problem 6 in 1.3
« Reply #1 on: September 23, 2018, 05:56:09 PM »
A linear differential equation is in the form of $a_0(t)y^{(n)} + a_1(t)y^{(n-1)}+ ... + a_n(t)y = g(t)$, 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.
« Last Edit: September 23, 2018, 05:57:42 PM by Wei Cui »