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) $\mathit{y}\mathbf{=}\mathbf{2}{\mathit{x}}^{\mathbf{2}}$

$\mathit{y}\mathbf{\text{'}}\mathbf{=}\mathbf{2}$

Short answer

Answer:

The solution is $y=2x$.

Step-by-step solution

Check if y=0 is a solution.

Put $y=0$into the given differential equation and simplify.

role="math" localid="1655460292516" $$\begin{gathered} \left(0\right)\text{'}=2 \\ 0=2 \\ 0\ne 2 \end{gathered}$$

This solution does not satisfy the given differential equation. Therefore, it is not a solution.

Check if y=2 is a solution.

Put $y=2$into the given differential equation and simplify.

$$\begin{gathered} \left(2\right)\text{'}=2 \\ 0=2 \\ 0\ne 2 \end{gathered}$$

This solution does not satisfy the given differential equation. Therefore, it is not a solution.

Check if y=2x is a solution.

Put $y=2x$into the given differential equation and simplify.

role="math" localid="1655460530440" $$\begin{gathered} \left(2x\right)\text{'}=2 \\ 2x=2 \\ 2=2 \end{gathered}$$

This solution satisfies the given differential equation. Therefore, it is a solution.

Check if y=2x2 is a solution.

Put $y=2x^2$into the given differential equation and simplify.

$$\begin{gathered} \left(2x^2\right)\text{'}=2 \\ 4x=2 \\ 4x\ne 2 \end{gathered}$$

This solution does not satisfy the given differential equation. Therefore, it is not a solution.