Order and Degree of differential equation

In this post we define Order and Degree of differential equation and also related examples and method to find the order and degree.

Order of differential equation

The order of differential equation is the order of the highest derivative appearing in the equation.

Degree of differential equation

The degree of the differential equation is the greatest exponent of the highest order derivative that appears in the equation.

Find Order and Degree of following differential equation

1.   $\frac{dy}{dx}+ycosx=sinx$
2.                $\frac{dy}{dx}=7x+5$
3. $\frac{dy}{dx}=cosx$
4. $\frac{d^2y}{dx^2}+xy&space;\left&space;(&space;\frac{dy}{dx}&space;\right&space;)^2=0$
5. $\left&space;[1+&space;\left&space;(\frac{dy}{dx}&space;\right&space;)^2&space;\right&space;]^{3/2}=\frac{d^2y}{dx^2}$
6. $\frac{dy}{dx}&space;+\left&space;[1+&space;\left&space;(\frac{dy}{dx}&space;\right&space;)^2&space;\right&space;]^{3/2}=0$
7. $\frac{d^2y}{dx^2}+\lambda&space;y=0$
8. $y^2&space;\frac{\partial&space;z}{\partial&space;x}+y&space;\frac{\partial&space;z}{\partial&space;y}=ax$
9. $x&space;\frac{\partial&space;z}{\partial&space;x}+y&space;\frac{\partial&space;z}{\partial&space;y}=nx$
10. $\frac{\partial^2&space;u}{\partial&space;x^2}+&space;\frac{\partial^2u}{\partial&space;y^2}+&space;\frac{\partial^2u}{\partial&space;z^2}=0$

Solution of  Order and Degree of following differential equation

1. order 01, degree 01
2. order 01, degree 01
3. order 01, degree 01
4. order 02, degree 01
5. order 02, degree 02     see solution
6. order 01, degree 06     see solution
7. order 02, degree 01
8. order 01, degree 01
9. order 01, degree 01
10. order 02, degree 01