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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.

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Step by step text solution for 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. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

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

    A
    `y=(x^(2)+c)/(4x^(2))`
    B
    `y=(x^(2))/4+c`
    C
    `y=(x^(4)+c)/(x^(2))`
    D
    `y=(x^(4)+c)/(4x^(2))`

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

    A
    `y=e^(x-y)-x^(2)e^(-y)+c`
    B
    `e^(y)-e^(x)=(x^(3))/3+c`
    C
    `e^(x)+e^(y)=(x^(3))/3+c`
    D
    `e^(x)-e^(y)=(x^(3))/3+c`

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

    A
    `y=tan^(-1)x`
    B
    `y-x=k(1+xy)`
    C
    `x=tan^(-1)y`
    D
    `tan(xy)=k`

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