Question

56) Find the order of the differential equation sin

dy

dx + x = y

57) Find the degree of the differential equation sin

dy

dx +

dy

dx =0.

58) Find the degree of the differential equation cos

dy

dx = x

59) Find the order of the differential equation y = px + √(1 + p2) where p =

dy

dx

60) If

dx

dy

= y +3˃0 and y(0) = 2, then find y(log2).

Answer 1

56) $\sin \left(\frac{dy}{dx}+x\right)=y$$\sin \left(\frac{dy}{dx}+x\right)=y$
Order is 1.

57) $\sin \left(\frac{dy}{dx}+\frac{dy}{dx}\right)=0$
Degree cannot be defined as the given differential equation is not a polynomial differential equation.

58) $\cos \left(\frac{dy}{dx}\right)=x$
Degree cannot be defined as the given differential equation is not a polynomial differential equation.

59) $y=x\left(\frac{dy}{dx}\right)+\sqrt{\left\{1+{\left(\frac{dy}{dx}\right)}^2\right\}}$
Order is 2.