Introduction ODE

Determine the order and degree for the following equation
 $5\left(\frac{\text{d}^4x}{\text{d}y^4}\right)^3+7\left(\frac{\text{d}x}{\text{d}y}\right)^{10}+y=x$  

• Order 1, Degree 10

• Order 1, Degree 3

• Order 4, Degree 10

• Order 4, Degree 3

Determine the order for the following equation $16y^{\left(4\right)}-t^6y^{''}-4y^5=3\cos t$  

• 4

• 6

• 2

• 5

For the following differential equations identify whether or not the equation is linear or non-linear  $y^2\frac{\text{d}^2y}{\text{d}x^2}+3\frac{\text{d}y}{\text{d}x}+y=e^x$  

• linear

• non-linear

Identify whether or not the equation is linear or non-linear $x^2\frac{\text{d}^2t}{\text{d}x^2}+x\frac{\text{d}t}{\text{d}x}+2t=\sin x$  

• linear

• non-linear

Determine whether or not the equation is linear or non-linear  $\frac{\text{d}^2y}{\text{d}t^2}+\cos y=1$  

• linear

• non-linear

Determine whether or not the equation is linear or non-linear  $5\left(\frac{\text{d}y}{\text{d}x}\right)^2-4y=e^x$  

• linear

• non-linear

Identify the independent variable  $x^2\frac{\text{d}^2t}{\text{d}x^2}+x\frac{\text{d}t}{\text{d}x}+2t=\sin x$  

• t

• x

Identify the independent variable for the following equation $\left(1-y^2\right)\frac{\text{d}x}{\text{d}y}+y\frac{\text{d}x}{\text{d}y}=1$  

• y

• x

State the order of the following equation and determine whether the equation is  linear or non-linear $xy^{\left(4\right)}+\tan\left(2+x\right)y^{''}=\ln x$  

• order 2, linear

• order 2, non-linear

• order 4, linear

• order 4, non-linear