2.(a) Solve the following initial value problem: (dy/dt) + 0.5ty = 2t with(0)=3. y = ?

(b) Find the general solution of the first-order linear differential equation: y' - (lnx)y = 3x^x .So y(x) = ? Note: UseCfor the arbitrary constant.

(c) Solve the initial-value problem(/) = ⁶ 5, (0)=2. Therefore y(x) = ?

(d) Find the general solution to tln(t)(dr/dt) + = 9te^t. Therefor r = ? UseCto denote the arbitrary constant in your answer.

(e) Find the solution to the initial value problem (1+x¹³)y'+13x¹²y=20x¹⁵. Subject to the conditiony(0)=2.

(f) Find the function y(t)that satisfies the differential equation (dy/dt) - 2ty = 9t²e^t2

At the end of the equation e is to the power of t^2 so (e^(t^2)). and the condition y(0)=2. So y(t) = ?

(g) Solve the initial-value problemtlnt(dy/dt)+y = te^t, y(2) = 1. So y(t) = ?