# GATE 2015 EE – SET 2 – Question 28

Solution:

$$\frac{di}{dt}$$ -0.2i = 0
$$\frac{1}{i}\frac{di}{dt}$$=0.2
$$\int \frac{1}{i}di$$ = $$\int$$0.2dt

ln(i) = 0.2t + c

i =$$e^{0.2t}$$ + c
i = $$e^{0.2t}$$*$$e^{c}$$
i = $$e^{0.2t}$$* $$C_{1}$$ ——–(1)
i(4) = 10 $$\Rightarrow$$ i = 10 ; t = 4

10 =$$e^{0.2(4)}$$ *$$C_{1}$$
$$C_{1}$$ = 10 $$e^{-0.8}$$

i =$$e^{0.2t}$$* $$C_{1}$$
i = $$e^{0.2t}$$* $$10e^{-0.8}$$
i = 10$$e^{0.2t-0.8}$$———(2)

i(-5) $$\Rightarrow$$ t = -5 into (2)

i(-5) = 10 $$e^{0.2(-5)}$$ – 0.8 = 10$$e ^{-1-0.8}$$ =10 $$e^{-1.8}$$=1.653