Question

General solution of a differential equation is $y=k{e}^x$. Find the particular solution if the curve passes through (0,1)

• A. $y=k{e}^x$
• B. $y=k{e}^x+C$
• C. $y=e^x$
• D. $y=2e^x$

Answer 1

The correct option is C $y=e^x$

We get particular solution from general solution when we assign values to the arbitrary constants based on the conditions. In this case the condition given is ‘the curve passes through (0,1). So we will substitute the point (0,1) in the given equation $y=k{e}^x$.
1 = k . 1
$\Rightarrow k=1$
So the particular solution is $y=e^x$