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If \(\rm \frac{\mathrm{d} y}{\mathrm{d x}} -4y = 0\), find the solution of the differential equation if, y(0) = 1
1. y = 4ex
2. y = e4x
3. y = e-4x
4. y = ex + 4

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Correct Answer - Option 2 : y = e4x

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

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