Home
Class 12
MATHS
If (y(1),y(2)) are two solutions of the ...

If `(y_(1),y_(2))` are two solutions of the differential `(dy)/(dx)+p(x).y=Q(x)` Then prove that `y=y_(1)+C(y_(1)-y_(2))` is the genral solution of the equation where C is any constant. For what relation between the constant `alpha,beta` will the linear combination `alphay_(1)+betay_(2)` also be a Solution.

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|10 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|15 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Solved Examples|1 Videos
  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

If y_1 and y_2 are two solutions to the differential equation (dy)/(dx)+P(x)y=Q(x) . Then prove that y=y_1+c(y_1-y_2) is the general solution to the equation where c is any constant.

If y_1 and y_2 are two solutions to the differential equation (dy)/(dx)+P(x)y=Q(x) . Then prove that y=y_1+c(y_1-y_2) is the general solution to the equation where c is any constant.

Solution of the differential equation (dy)/(dx)+(2y)/(x)=0 , where y(1)=1 , is

The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2) , is

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

Let y_(1) and y_(2) be two different solutions of the equation (dy)/(dx)+P(x).y=Q(x) . Then alphay_(1)+betay_(2) will be solution of the given equation if alpha + beta=……………….

The solution of the differential equation log(dy/dx)=4x-2y-2,y=1 ,where x=1 is

The solution of the differential equation x(dy)/(dx) + 2y = x^2 (X ne 0) with y(1) =1, is :

The solution of the differential equation, dy/dx=(x-y)^(2) , when y(1)=1, is

If y(x) is the solution of the differential equation ( dy )/( dx) +((2x+1)/(x))y=e^(-2x), x gt 0 , where y(1) = (1)/(2) e^(-2) , then