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Ordinary Differential Equations 3 Mark Book Back Question Paper With Answer Key

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 45

     3 Marks 

    15 x 3 = 45
  1. Find the differential equation of the family of circles passing through the points (a, 0) and (−a, 0).

  2. Solve \((1+{ x }^{ 2 })\frac { dy }{ dx } =1+{ y }^{ 2 }\)

  3. Find the particular solution of (1+ x3)dy − x2 ydx = 0 satisfying the condition y(1) = 2.

  4. Solve y' = sin2 (x − y + 1 ).

  5. Solve : \(\frac { dy }{ dx } =\sqrt { 4x+2y-1 } \)

  6. Solve \(\frac { dy }{ dx } =\frac { x-y+5 }{ 2(x-y)+7 } .\)

  7. Solve (x2 -3y2) dx + 2xydy = 0.

  8. Solve \(\left( y+\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \right) dx-xdy=0,\ y(1)=0\)

  9. Solve \((1+{ 2e }^{ x/y })dx+2{ e }^{ x/y }\left( 1-\frac { x }{ y } \right) dy=0\)

  10. Solve \(\frac { dy }{ dx } +2y={ e }^{ -x }\)

  11. Solve [y(1-x tan x)+x2 cosx] dx-dy = 0

  12. Solve the Linear differential equation:
    cos x\(\frac{dy}{dx}\)+y sin x = 1

  13. Solve the Linear differential equation:
    \((1-{ x }^{ 2 })\frac { dy }{ dx } -xy=1\)

  14. Solve the Linear differential equation:
    \(\frac { dy }{ dx } +\frac { y }{ x } =sinx\)

  15. If M(x, y) dx + N(x, y) dy = 0 is a homogeneous equation, then the change of variable y = vx, transforms into a separable equation in the variables v and x

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