Question

In Problems 7–12 match each of the given differential equations with one or more of these solutions:

(a) $\mathit{y}\mathbf{=}\mathbf{0}$, (b) $\mathit{y}\mathbf{=}\mathbf{2}$, (c) $\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}$, (d) $\mathit{y}\mathbf{=}\mathbf{2}{\mathit{x}}^{\mathbf{2}}$

$\mathit{y}\mathbf{"}\mathbf{+}\mathbf{9}\mathit{y}\mathbf{=}\mathbf{18}$

Short answer

Answer:

The solution is$y=2$.

Step-by-step solution

Check  if is a solution.

Put $y=0$.

$$\begin{gathered} \left(0\right)"+9\left(0\right)=18 \\ 0=18 \\ 0\ne 18 \end{gathered}$$

Hence, it is not a solution.

Check y=2 if is a solution.

Put $y=2$.

$$\begin{gathered} \left(2\right)"+9\left(2\right)=18 \\ 0+18=18 \\ 0=18 \end{gathered}$$

Hence, it is a solution.

Check y=2xif is a solution.

Put $y=2x$.

$$\begin{gathered} \left(2x\right)"+9\left(2x\right)=18 \\ 0+18x=18 \\ 18x\ne 18 \end{gathered}$$

Hence, it is not a solution.

Check y=2x2 if is a solution.

Put $y=2x^2$.

$$\begin{gathered} \left(2x^2\right)"+9\left(2x^2\right)=18 \\ \left(4x\right)"+18x^2=18 \\ 4+18x^2\ne 18 \end{gathered}$$

Hence, it is not a solution.