Correct Answer - Option 2 : y = e
4x
Concept:
For first-order differential equation, separate the variable and integrate accordingly.
Put the given condition to find out the integration constant
Calculation:
Given differential equation
\(\rm \frac{\mathrm{d} y}{\mathrm{d x}} -4y = 0\)
⇒ \(\rm \frac{\mathrm{d} y}{y} =4dx\)
Integrating both sides
⇒ \(\rm \int\frac{\mathrm{d} y}{y} =\int4dx\)
⇒ ln y = 4x + c
⇒ y = e4x + c
Now y(0) = 1
⇒ 1 = e0 + c
⇒ c = 0
∴ y = e4x