Question

Find the solution of the differential equation that satisfies the given initial condition. dL = klin(t), L(1) = -1 dt -1 k[In(t) - 1+1] + 1 X

Answer 1

☆ Given dh dt Kih² lnct) 2012-1 = k Inst) dt dL 22 + c kllo(t) dit to Integrate on both sides Stadt= kſ lnct) dt 4. kſ loitat Si. lnltlat eftg'= fg - Sf g f = lncat g.1 f = g=t 11 : tlolt) -S7'dt t(ln(t)-1) + go (6) - t from 0 = K tlln(t)-1) + Initial Condeton: L(1)=-1 when tal then L--1 1:loli) = 0 - = k (1) ( loco) -10) + 1 = K (0-1) + c Ca 1+R -1 from 0 Ź - Kt(lnce)-1) +(1+k) 36 = k[t In(t)- t +1]+,