The solution of \(\rm {dx\over dt}= 3x+8\) will be

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Navik GD 2022 (All Shift) Memory Based Paper (Section I + II)

Answer 1

Concept:

Some useful formulas are:

\(\rm \int{dx\over ax}={1\over a}logx+c\)

If log x = z then we can write x = e^z

Calculation:

\(\rm {dx\over dt}= 3x+8\)

Rearranging the equation and integrating we get,

⇒\(\rm \int{dx\over 3x+8}=\int dt\)

⇒\(\rm {1\over 3 }log({3x+8})=t+c\), c = constant of integration

⇒ log(3x + 8) = 3(t + c)

⇒ 3x + 8 = e^3(t+c)

⇒ 3x = e^3(t+c) - 8

∴ \(\rm x ={ 1\over 3}e^{3(t+c)}-{8\over 3}\)