Home
Class 12
MATHS
For each of the following differential e...

For each of the following differential equations, verify that the accompanying function is a solution in the domain mentioned ( `A, B in R`: parameters)
(i) `xy'=y(x in R \\{0}):Ax(x in R\\{0})`
(ii) `x^(3)y''=1(x in R \\{0}):(1)/(2x)+Ax+B(x in R \\{0})`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise Frequently Asked Questions|46 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise Questions From NCERT Exemplar (Example)|3 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Chapter test 4|12 Videos

  • INTEGRALS

    MODERN PUBLICATION|Exercise COMPETITION FILE|24 Videos

Similar Questions

Explore conceptually related problems

For each of the following differential equations, verify that the accompanying functions is a solution ( both the differential equations and the accompanying functions being on whole of R ) : (i) y'=e^(x):e^(x) (ii) (1+x^(2))y'=xy: sqrt(1+x^(2)) .

Verify that the given function is a solution of the corresponding differential equation: y=Ax: xy\'=y (x!=0)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : y=Ax : xy'=y(x ne 0)

Verify that each of the following functions y:R rarr R , as defined below, is the solution of the accompanying initial value problems : y=e^(x):y'=y, y(0)=1

Verify that each of the following functions y:R rarr R , as defined below, is the solution of the accompanying initial value problems : y= cos x (x in R): y''+y=0, y(0)=1, y'(0)=0 .

Verify that each of the following functions y:R rarr R , as defined below, is the solution of the accompanying initial value problems : y=x^(2)+2x+1, y'''=0, y(0)=1, y'(0)=2, y''(0)=2

Differentiate the following functions w.r.t.x : ax^(2)+2by^(2)+3hxy=0

Which of the following relations is not symmetric? R_(1), on R defined by (x,y)in R_(1)hArr1+xy>0 for all x,y in R

A function f:R rarr R satisfies the differential equation 2xy+(1+x^(2))y'=1 where f(0)=0 then

A function f : R to R Satisfies the following conditions (i) f (x) ne 0 AA x in R (ii) f(x +y)= f(x) f(y) AA x, y, in R (iii) f(x) is differentiable (iv ) f'(0) =2 The value of f(0) is