2. ORDER
The order of a differential equation is the order of the
highest order derivative present in the equation.
o To find the order
First find the derivative
Pick the highest one
Take the order of the highest one
3. FIND THE ORDER OF 𝑥𝑦
𝑑2 𝑦
𝑑𝑥2 + 𝑥
𝑑𝑦
𝑑𝑥
3
− 𝑦
𝑑𝑦
𝑑𝑥
= 0
Here the highest order derivative present in the given differential
equation is
𝒅 𝟐 𝒚
𝒅𝒙 𝟐 and its order is 2
So the order of the given differential equation is 2
4. FIND THE ORDER OF THE FOLLOWING
DIFFERENTIAL EQUATIONS:
1.
𝑑𝑦
𝑑𝑥
= sin 𝑥
2.
𝑑3 𝑦
𝑑𝑥3
3
− 𝑥𝑦
𝑑𝑦
𝑑𝑥
4
+ 𝑦 = 0
3.
𝑑2 𝑦
𝑑𝑥2 +
3
1 +
𝑑𝑦
𝑑𝑥
3
= 0
5. DEGREE
The degree of a differential equation is the highest power of highest
order derivative when the differential equation is a polynomial equation
in derivatives which are free from fractions and radicals
o To find the degree
Check whether the given diff. eqn. is a polynomial in derivatives or not
Check whether derivatives are free from fractions and radicals or not
Find the highest order derivative and take its power or degree
6. FIND THE DEGREE OF 𝑥𝑦
𝒅 𝟐 𝒚
𝒅𝒙 𝟐 + 𝑥
𝑑𝑦
𝑑𝑥
3
− 𝑦
𝑑𝑦
𝑑𝑥
= 0
Here the highest order derivative present in the given differential
equation is
𝒅 𝟐 𝒚
𝒅𝒙 𝟐 and its power is 1
So the degree of the given differential equation is 1
7. FIND THE DEGREE OF
𝑑2 𝑦
𝑑𝑥2 + 1 +
𝑑𝑦
𝑑𝑥
3
= 0
Solution:
𝑑2 𝑦
𝑑𝑥2
+ 1 +
𝑑𝑦
𝑑𝑥
3
= 0 𝑜𝑟,
𝑑2 𝑦
𝑑𝑥2
= − 1 +
𝑑𝑦
𝑑𝑥
3
𝑜𝑟,
𝑑2 𝑦
𝑑𝑥2
2
= 1 +
𝑑𝑦
𝑑𝑥
3
Here the highest order derivative present in the given differential equation is
𝑑2 𝑦
𝑑𝑥2 and its power is 2
So the degree of the given differential equation is 2
8. FIND THE DEGREE OF
𝑑2 𝑦
𝑑𝑥2
2
+ COS
𝑑𝑦
𝑑𝑥
= 0
The given differential equation is not a polynomial equation
in
𝑑𝑦
𝑑𝑥
So its degree is not defined
9. FIND THE DEGREE OF THE FOLLOWING
DIFFERENTIAL EQUATIONS:
𝑑𝑦
𝑑𝑥
= sin 𝑥
𝑑3 𝑦
𝑑𝑥3
3
− 𝑥𝑦
𝑑𝑦
𝑑𝑥
4
+ 𝑦 = 0
𝑑2 𝑦
𝑑𝑥2 +
3
1 +
𝑑𝑦
𝑑𝑥
3
= 0
