Degree of Differential Equations

In this page degree of differential equations we are going to see some practice questions of how to find order and degree of a given differential equations.

Find the order and degree of the following differential equations.

(i) (dy/dx) + y = x²

(ii) y' + y² = x

(iii) y'' + 3 y'² + y³

(iv) d²y/dx² + x = √[y + (dy/dx)]

(v) d²y/dx² - y + (dy/dx + d³y/dx³)^(3/2) = 0

(vi) y'' = (y - y'³)^(2/3)

(vii) y' + (y'')² = (x + y'')²

(viii) y' + (y'')² = x (x + y'')²

(ix) (dy/dx)² + x = (dx/dy) + x²

Solution for above practice questions

(i) (dy/dx) + y = x²

Solution:

Here the given differential equation of variable "y" is differentiable with respect to "x" maximum one time. From this we can decide that the order of the given differential equation is 1 and its highest power is 1 so degree is also 1.

 Order = 1

 Degree = 1


(ii) y' + y² = x

Solution:

Here the given differential equation of variable "y" is differentiable with respect to "x" maximum one time. From this we can decide that the order of the given differential equation is 1 and its highest power is 1 so degree is also 1.

 Order = 1

 Degree = 1


(iii) y'' + 3 y'² + y³

Solution:

Here the given differential equation the variable "y" is differentiable with respect to "x" maximum two times. From this we can decide that the order of the given differential equation is 2 and its highest power is 1 so degree is also 1.

Order = 2

Degree = 1


(iv) d²y/dx² + x = √[y + (dy/dx)]

Solution:

Since the given differential equation is having square root. We have to remove the square root,for that we are going to take squares on both sides

(d²y/dx² + x)² = (√[y + (dy/dx)])²

(d²y/dx² + x)² = [y + (dy/dx)]

Order = 2

Degree = 2


(v) d²y/dx² - y + (dy/dx + d³y/dx³)^(3/2) = 0

Solution:

d²y/dx² - y + (dy/dx + d³y/dx³)^(3/2) = 0

d²y/dx² - y = - (dy/dx + d³y/dx³)^(3/2)

Now we are going to take squares on both sides

[d²y/dx² - y]² = (- (dy/dx + d³y/dx³)^(3/2))²

[d²y/dx² - y]² = (dy/dx + d³y/dx³)^(3/2) x 2

[d²y/dx² - y]² = (dy/dx + d³y/dx³)³

y is differentiable with respect to x maximum three times.So the order is 3 and the highest power is 3. So its degree is 3.

Order = 3

Degree = 3

degree of differential equations degree of differential equations