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By substituting y = vx, the solution of ...

By substituting y = vx, the solution of the differential equation
`(dy)/(dx)-(x^(2)+y^(2))/(xy)=0`, is

A

`x^(2)y^(2)=logx+C`

B

`(y^(2))/(2x^(2))=logx+C`

C

`(2y^(2))/(x^(2))=logx+C`

D

`(y^(2))/(x^(2))=logx+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Substituting y = vx and `(dy)/(dx)=v+x(dv)/(dx)` in the given differential equation, we get
`v+x(dv)/(dx)=(1+v^(2))/(v)rArrx(dv)/(dx)=(1)/(v)rArrvdv=(1)/(x)dx`
On integrating, we get
`(v^(2))/(2)=logx+CrArr(y^(2))/(2x^(2))=logx+C`
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIAL EQUATIONS-Chapter Test
  1. By substituting y = vx, the solution of the differential equation (d...

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  2. (x^(2)+y ^(2)) dy = xydx. If y (x (o)) =e, y (1)=1, then the value of ...

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  3. The differential equation of the family of curves y^(2)=4xa(x+1), is

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  4. y=ae^(mx)+be^(-mx) satisfies which of the following differential equat...

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  5. The solution of the differential equation (dy)/(dx)=e^(y+x)+e^(y-x), i...

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  6. The differential equation of the family of curves y=e^(2x)(a cos x+b s...

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  7. The differential equation obtained on eliminating A and B from y=A c...

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  8. The solution of (dy)/(dx)=((y)/(x))^(1//3), is

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  9. The slope of the tangent at (x , y) to a curve passing through a po...

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  10. Solve Y-X(dy)/(dx)=a(y^(2)+(dy)/(dx))

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

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  12. The general solution of the differential equation (dy)/(dx)+sin((x+y)/...

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  13. The solution of (dy)/(dx)-y=1, y(0)=1 is given by

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  14. The number of solution of y'=(x+1)/(x-1),y(1)=2, is

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  15. What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0?

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  16. Solution of the differential equation x(dy)/(dx)=y+sqrt(x^(2)+y^(2)), ...

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  17. Integral curve satisfying Y'=(x^2 +y^2)/(x^2-y^2) y' (1) ne 1 has th...

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  18. The differential equation which represents the family of plane curves ...

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  19. A continuously differentiable function y=f(x) , x in ((-pi)/(2) ,(pi)/...

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  20. The solution of the differential equation (d^(2)y)/(dx^(2))=e^(-2x), i...

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  21. The order and degree of the differential equation (d^(2)y)/(dx^(2))=sq...

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