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Prove that the equation x62(dy)/(dx)=x^2...

Prove that the equation `x62(dy)/(dx)=x^2-2y^2+xy` is a homogenous differential equation

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x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

Verify that the function y = e^(2x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0

Knowledge Check

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

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

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

    A
    `1/(x+y)=c`
    B
    `sin^(-1)(x+y)=x+c`
    C
    `tan^(-1)(x+y)=c`
    D
    `tan^(-1)(x+y)=x+c`

  • The solution of 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)`

    • Similar Questions

    Explore conceptually related problems

    Solve the differential equation x(dy)/(dx)+2y=xlogx .

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

    Show that the differentia equation (xe^(y//x) + y) dx = x dy is homogeneous. Find the particular solution of this differential equation, given that x = 1 when y = 1.

    Show that the differential equation [x sin^(2)((y)/(x)) - y]dx+x dy = 0 is homogeneous. Find the particular solution of this differential equation, given that y = (pi)/(4) when x = 1.

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

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