In this page degree of differential equations1 we are going to see solution of some practice questions.

(vi) y'' = (y - y'³)^(2/3)

Solution:

In the first step we are going to take cubes on both sides

(y'')³ = [(y - y'³)^(2/3)]³

(y'')³ = (y - y'³)^(2/3) x 3

(y'')³ = (y - y'³)²

The given differential equation of variable y is differentiable with respect to x maximum two times. So the order is 2. The highest power is 3. So degree is 3.

Order = 2

Degree = 3

(vii) y' + (y'')² = (x + y'')²

Solution:

y' + (y'')² = (x + y'')²

now we are going to expand the right side term using the algebraic formula (a + b)² = a² + 2 ab + b²

y' + (y'')² = x² + (y'')² + 2 x y''

y' + (y'')² - x² - (y'')² - 2 x y'' = 0

y' - x² - 2 x y'' = 0

The given differential equation of variable y is differentiable with respect to x maximum two times. So the order is 2. The highest power is 1. So degree is 1.

Order = 2

Degree = 1

(viii) y' + (y'')² = x (x + y'')²

Solution:

y' + (y'')² = x(x + y'')²

now we are going to expand the right side term using the algebraic formula (a + b)² = a² + 2 ab + b²

y' + (y'')² = x [x² + (y'')² + 2 x y'']

y' + (y'')² = [x³ + x (y'')² + 2 x²y'']

y' + (y'')² - x³ - x (y'')² - 2 x² y'' = 0

The given differential equation of variable y is differentiable with respect to x maximum two times. So the order is 2. The highest power is 2. So degree is 2.

Order = 2

Degree = 2

(ix) (dy/dx)² + x = (dx/dy) + x²

Solution:

(dy/dx)² + x = (dx/dy) + x²

(dy/dx)² + x = 1/(dy/dx) + x²

(dy/dx)² + x = [1 + x²(dy/dx)]/(dy/dx)

(dy/dx)[(dy/dx)² + x] = [1 + x²(dy/dx)]

(dy/dx)³ + x (dy/dx) = [1 + x²(dy/dx)]

Here the given differential equation of variable y is differentiable with respect to x maximum one time. So the order is 1. The highest power is 3. So we can say that degree is 3.

Order = 1

Degree = 3

degree of differential equations1 degree of differential equations1

- Practice questions of order and degree
- Substitution method
- Decomposition method
- Properties of integrals
- Integration-by parts
- Integration-of Sec³ x
- Standard integrals
- Integrating quadratic denominator
- Integration-using partial fractions
- Definite integrals