If \(\rm \frac{\mathrm{d} y}{\mathrm{d x}} -4y = 0\), find the solutio

1.	If \(\rm \frac{\mathrm{d} y}{\mathrm{d x}} -4y = 0\), find the solution of the differential equation if, y(0) = 11. y = 4ex2. y = e4x3. y = e-4x4. y = ex + 4
Answer» 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 = e^{4x + c} Now y(0) = 1 ⇒ 1 = e^{0 + c} ⇒ c = 0 ∴ y = e^4x

If \(\rm \frac{\mathrm{d} y}{\mathrm{d x}} -4y = 0\), find the solution of the differential equation if, y(0) = 11. y = 4ex2. y = e4x3. y = e-4x4. y = ex + 4

Answer» 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 = e^{4x + c}

Now y(0) = 1

⇒ 1 = e^{0 + c}

⇒ c = 0

∴ y = e^4x

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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) = 11. y = 4ex2. y = e4x3. y = e-4x4. y = ex + 4

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