Question
Differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\text{y}=0,\text{y}(0)=2,\text{y}'(0)=0$
Function
$\text{y}=\text{e}^\text{x}+\text{e}^{-\text{x}}$Function
$\text{y}=\text{e}^\text{x}+\text{e}^{-\text{x}}$$\Rightarrow\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{y}=0$
It is the given differential equation.Therefore,
y = ex + e-x satisfies the given differential equation.Also, when x = 0; = e
0 + e0 = 1 + 1, i.e. y(0) = 2. And, when x = 0; y1 = e0 - e0 = 1 - 1, i.e. y'(0) = 0 Hence, y = ex + e-x is the solution to the given initial value problem.Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.