Differential Equations — Maths STD 12 Science — Question

y=e^x ...(1) Differentiating both sides of (1)with respect to x, we get

$=\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}}$

$=\frac{\text{dy}}{\text{dx}}=\text{y}$ [Using (1)]

It is the given differential equation.

Here, y = ex satisfies the given differential equation; hence, it is a solution.

Also, when x = 0, y = e⁰ = 1, i.e. y(0) = 1

Hence, y = e^x is the solution to the given initial value problem.