(Need help for Review sheet) Some practice problems:
For each problem below, clearly identify the type of equation: Linear Equation, Separable Equation, Bernoulli Equation, Nonlinear Homogeneous Equation, or Exact Equation. Find the general solution (give an explicit solution unless instructed otherwise). If there is an initial condition given, also find the particular solution satisfying the condition.
(1)/(t^(3))(dy)/(dt)=(1)/(y^(4))
ty' - 5y = t^(4)y^(3)
y' + 6y = -(2t + 12e^(-5t)), y(0) = -10
15x^(2)y^(4) + e^(x)sin(y) + (20x^(3)y^(3) + e^(x)cos(y) + (1)/(y+1))y' = 0, solve implicitly
y' = (-6 - 3x)y^(2), y(0) = (2)/(9) (give the interval of validity)
(t^(2) + 5)(dy)/(dt) = t(81 + y^(2))
(dy)/(dx) = (x^(2) + 5y^(2))/(7xy), solve implicitly
xy' = 8xsin(3x) - y
