Home
Class 12
MATHS
Find the real value of m for which the s...

Find the real value of `m` for which the substitution `y=u^m` will transform the differential equation `2x^4y(dy)/(dx)+y^4=4x^6` in to a homogeneous equation.

Text Solution

Verified by Experts

`y=u^(m)`
or `(dy//dx) = mu^(m-1)(du)/(dx)`
The given differential equation becomes
`2x^(4).u^(m). Mu^(m-1)(du)/(dx) +u^(4m)=4x^(6)`
for homogenous equation, degree of each term should be same in the numerator and the denominator. Hence,
`6=4m=4+2m-1` or `m=3//2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Solve the differential equation : (dy)/(dx)-y/x=2x^2

Show that the differential equation y^3dy+(x+y^2)dx=0 can be reduced to a homogeneous equation.

Find y(x) from the differential equation (dy)/(dx)-x^2y = 0 ,

Show that the differential equation (x - y) (dy)/(dx) = x + 2y is homogeneous and solved it.

The solution of the differential equation (x+2y^3)((dy)/(dx))=y is

The solution of the differential equation (dy)/(dx)=e^(2x+y) is

Solve the differential equation (x)dy = ( 1 + y^(2))dx .

The solution of the differential equation (x+2y^(3))(dy)/(dx)=y is -

The solution of the differential equation (dy)/(dx)=(x-y)/(x+y) is -

The solution of the differential equation (x+y)(dx-dy)=dx+dy is -