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y = log x + c is a solution of the diff...

`y = log x + c ` is a solution of the differential equation ` x(d^(2)y)/(dx^(2)) + (dy)/(dx) = 0`

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To verify that \( y = \log x + c \) is a solution of the differential equation \[ x \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0, \] we will follow these steps: ...
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Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0

Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^(2)(d^(2)y)/(dx^(2))+(dy)/(dx)+y=0

Knowledge Check

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

    A
    `log|y|=(1)/(2)x^(2)-x+c`
    B
    `log|y|=(1)/(2)x^(2)+x+c`
    C
    `log|y|=(1)/(3)x^(2)-x+c`
    D
    `log|y|=(1)/(3)x^(2)+x+c`

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

    A
    y=1+cxy
    B
    y=log (cxy)
    C
    y+1 = cxy
    D
    y=c+xy

  • Solution of the differential equation y dx+(x-y^(2))dy=0 is

    A
    `xy+y^(3)=c`
    B
    `xy-y^(3)=c`
    C
    `3xy+y^(3)=c`
    D
    `3xy-y^(3)=c`

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