For Problems $1-6,$ determine whether the differential equation is linear or nonlinear.

$\frac{d^{2}y}{d{x}^2}+e^x\frac{dy}{dx}=x^2.$

$\frac{d^{3}y}{d{x}^3}+4\frac{d^{2}y}{d{x}^2}+sinx\frac{dy}{dx}=x{y}^2+tanx.$

$y{y}^{\text{'}\text{'}}+x(y^{\text{'}})-y=4xlnx.$

$sinx*y^{\text{'}\text{'}}+y^{\text{'}}-tany=cosx.$

$\frac{d^{4}y}{d{x}^4}+3\frac{d^{2}y}{d{x}^2}=x.$

$\sqrt[\phantom{2}]{x}{y}^{\text{'}\text{'}}+\frac{1}{y^{\text{'}}}lnx=3x^3.$