If I have the ODE:

x`=x^{2}*e^{t}+e^{x}

can this differential equation be considered linear?

I know that the definition of a linear ODE is that it can be written as:

x`+a(t)x=b(t)

if I take the sqrt of my initial ODE than I have:

x'-(e^{t})^{(1/2)}*x=(e^{x})^{(1/2)}

This would be a linear differential equation with:

a(t)=(e^{t})^{(1/2)}and

b(t)=(e^{x})^{(1/2)}

is this true?