Classification of Differential Equations

Classify the following in terms of order and linearity;
 $\frac{d^2y}{dx^2}+4\sin y=5x+2$  

• First order non-linear 

• Second order linear

• Second order non linear

• First order linear

Classify the following in terms of order and linearity
 $\frac{d^2y}{dx^2}+\frac{dy}{dx}+3y=x$  

• First order non linear

• First order linear

• Second order non linear

• Second order linear

Classify the following in terms of linearity and order
 $3x^2y''+2\ln\left(x\right)y'+e^xy=3x\cos x$  

• Second order non linear

• Second order linear

• First order linear

• First order non linear

Classify the following in terms of order and linearity
 $4yy'-x^3y'+\cos y=e^{2x}$  

• First order linear

• First order non linear

• Second order non linear

• Second order linear

Classify the following in terms of order and linearity
 $y''+2y'+e^y=x$  

• First order non linear

• Second order non linear

• First order linear

• Second order linear