Question

The solution of the differential equation $\frac{d^{2}y}{d{x}^2}=0$ with boundary conditions

(i) $\frac{dy}{dx}=1atx=0$

(ii) $\frac{dy}{dx}=1atx=1$ is

• A. y = 1
• B. y = x
• C. y = x + c where c is an arbitrary constants
• D. y = $C_{1}x+C_2$ where $C_1,C_2$ are arbitary constants

Answer 1

The correct option is C y = x + c where c is an arbitrary constants

Given $\frac{d^{2}y}{d{x}^2}=0$ ...(i)

$\Rightarrow \frac{dy}{dx}=C_1\Rightarrow y=C_{1}x+C_2$

Using y'(0) = 1, we get

$C_1=1$

so general solution is y = x + $C_2$