The degree of the differential equation satisfying the relation `sqrt(1+x^2) + sqrt(1+y^2) = lambda (x sqrt(1+y^2)- ysqrt(1+x^2))` isA. 1B. 2C. 3D. None of these

The degree of the differential equation satisfying the relation `sqrt(

1.	The degree of the differential equation satisfying the relation `sqrt(1+x^2) + sqrt(1+y^2) = lambda (x sqrt(1+y^2)- ysqrt(1+x^2))` isA. 1B. 2C. 3D. None of these
Answer» Correct Answer - a On putting x = tan A and y = tan B in the given relation , we get ` cos A + cos B = lambda ( sin A - sinB)` ` rArr tan.((A-B)/2) = 1/lambda ` ` rArr tan^(-1) x - tan^(-1) y = 2 tan^(-1) (1/lambda )` On differentiating w.r.t x, we get `1/(1+x^(2)) - 1/(1+y^(2)) = 0 ` ` rArr (dy)/(dx) = (1+y^(2))/(1+x^(2))` Clearly , it is a differential equation of degree `

Discussion

No Comment Found

Related InterviewSolutions

Find the general solution of the differential equation `x(dy)/(dx)+2y=x^2(x!=0)`.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 `x+y(dy)/(dx)=2y` is
Solution of the differential equation `(dy)/(dx)=(y+sqrt(x^(2)-y^(2)))/(x)` isA. `sin^(-1)((x)/(y))-log|x|=c`B. `sin^(-1)((x)/(y))+log|x|=c`C. `sin^(-1)((y)/(x))-log|x|=c`D. `sin^(-1)((y)/(x))+log|x|=c`
Solution of the differential equation `(x^(2)-y^(2))dx-2xy dy=0` isA. `x^(2)-y^(2)=cx`B. `x^(2)+y^(2)=cx`C. `x^(2)-y^(2)=c`D. `x^(2)+y^(2)=c`
Show that the differential equation `2xy (dy)/(dx) = x^2+3y^2 ` is homogeneousand solve it.A. `x^(3)+y^(2)=cx^(2)`B. `(x^(2))/(2)+(y^(3))/(3)=y^(2)+c`C. `x^(2)+y^(3)=cx^(2)`D. `x^(2)+y^(2)=cx^(2)`
Solution of the differential equation `x^(2)y dx-(x^(3)+y^(3))dy=0` isA. `log|y|=(x^(3))/(3y^(3))+c`B. `log|y|=(-x^(3))/(3y^(3))+c`C. `log|y|=(x^(3))/(y^(3))+c`D. `log|y|=(-x^(3))/(y^(3))+c`
Solution of the differential equation `x(dy)/(dx)=y+sqrt(x^(2)+y^(2))`, isA. `y-sqrt(x^(2)+y^(2))=cx^(2)`B. `y+sqrt(x^(2)+y^(2))=cx^(2)`C. `y-sqrt(x^(2)+y^(2))=cx`D. `y+sqrt(x^(2)+y^(2))=cx`
Solution of the differential equation `x^(2)y dy+(x^(3)+x^(2)y-2xy^(2)-y^(3))dx=0` isA. `log|(y+x)/(x^(4)(y-x))|=(4x)/(x+xy)+c`B. `log|(y-x)/(x^(4)(y+x))|=(4x)/(x+xy)+c`C. `log|(y+x)/(x^(4)(y-x))|=(4x)/(x+y)+c`D. `log|(y-x)/(x^(4)(y+x))|=(2x)/(x+y)+c`
Solution of the differential equation `(x^(2)+2y^(2))dx-xy dy=0,` when y (9)=0 isA. `x^(4)=-81(x^(2)+y^(2))`B. `x^(4)=81(x^(2)+y^(2))`C. `x^(4)=-9(x^(2)+y^(2))`D. `x^(4)=9(x^(2)+y^(2))`
The solution of the differential equation ` xy^(2) dy - (x^(3) +y^(3))dx = 0 ` isA. `y^(3)=3x^(3)+c`B. `y^(3)=3x^(3)log|cx|`C. `y^(3)=3x^(3)+log|cx|`D. `y^(3)+3x^(3)=log|cx|`

The degree of the differential equation satisfying the relation `sqrt(1+x^2) + sqrt(1+y^2) = lambda (x sqrt(1+y^2)- ysqrt(1+x^2))` isA. 1B. 2C. 3D. None of these

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment