solve the following initial value problems:
dy/dt cos t + y sin t = 1 where y(Pi/4) = sqrt(2)
(1 + x^2) dy/dx = y where y(0) = 1
t* dy/dt - y = t^3 sin t where y(Pi) = 0
Divide through by to get
The integrating factor is (Verify)
Thus, the DE becomes
Can you take it from here??
Separating the variables, you have(1 + x^2) dy/dx = y where y(0) = 1
Can you take it from here?
Divide through by to gett* dy/dt - y = t^3 sin t where y(Pi) = 0
The integrating factor is
Thus, the DE becomes
Can you take it from here?
Does this make sense?