Thiele’s Differential Equation, solve analytically (using calculus) for the policy value 𝑡𝑉𝑥

I need assistance with solving this question.

Consider the following information for a given policy :

a. δ = 0. 03

b. Level premium 𝑝 = $3500

c. No expenses.

d. µ = 0. 0007

e. Benefit payment 𝑆 = $150, 000

(i) Using Thiele’s Differential Equation, solve analytically (using

calculus) for the policy value 𝑡𝑉𝑥.

(ii) Find the unique solution to this differential equation clearly

showing why this is the case.

(iii) Describe the what happens to the policy value as 𝑡 → ∞.

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