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 $y=e^x$