Since we have been discussing ODEs, it's a good opportunity to review some of the

standard analytical methods for solving ODEs.

Solve the following Initial Value Problems

1.dx/dt = 2x − 2t(linear) 2.^{2}− 3 , x(0) = 2dx/dt = tx + t(Bernoulli) 3.^{3}x^{2}, x(0) = 1dx/dt = 2x − 3y + 3e(linear system)^{t}, x(0) = 1dy/dt = − x + y − e^{t}, y(0) = 0