Question

1. Solve the differential equation

(4+t²)dy/dt + 2ty = 4t


2. Find the general solution of the differential equation dy/dt + (1/2)y = (1/2)e^t/3 .


3. Solve the initial value problem .
ty' + 2y = 4t² , where y(1) = 2.​

Answer 1

1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.

2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.

3. The solution to the initial value problem is y = t^2 + 4/3.