Home
Class 12
MATHS
If the solution of the differential equa...

If the solution of the differential equation `(dy)/(dx)=1/(xcosy+sin2y)` is `x=c e^(siny)-k(1+siny),` then the value of `k` is_______

Text Solution

Verified by Experts

The correct Answer is:
2
`(dy)/(dx) = 1/(xcosy+2sinycosy)`
`therefore (dx)/(dy) = xcosy+2sinycosy`
`therefore (dx)/(dy) +(-cosy)x=2sinycosy`
`therefore I.F. =e^(-intcosydx)=e^(-siny)`
Thus, the solution is
`x.e^(-siny)=2inte^(-siny).sinycosydy = -2sinye^(-siny)+2inte^(-siny)cosydy`
`=-2sinye^(-siny)+2inte^(-siny)cosydy`
`=-2sinye^(-siny)-2e^(-siny)+c`
i.e., `x=-2siny-2+ce^(siny)=ce^(siny)-2(1+siny)`
`therefore k=2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Matrix Match Type|3 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

If the solution of the differential equation (dy)/(dx)=(1)/(x cos y+sin2y) is x=ce^(sin y+sin2y) is y), then the value of k

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

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

The solution of the differential equation (dy)/(dx) = 1/(xy[x^(2)siny^(2)+1]) is

Solution of the differential equation sin^(-1)((dy)/(dx))=x+y is

Solution of the differential equation (x-y)(1-(dy)/(dx))=e^(x) is

The solution of the differential equation (dy)/(dx)=(1)/(xy[x^(2)sin y^(2)+1]) is

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

Solution of the differential equation (x(dy)/(dx)-y)sin((y)/(x))=x^(2)e^(x) is