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Differential Equations - Two Marks Study Materials

12th Standard

    Reg.No. :
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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Solve: \(\frac { dy }{ dx } \) = y sin 2x

  2. Solve the following differential equations: \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +16y=0\)

  3. Find the order and degree of the following differential equations.
    \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

  4. Find the differential equation of the following
    x2 + y2 = a2

  5. Write down the order and degree of the following differential equations.
    \(\left( \frac { dy }{ dx } \right) ^{ 3 }-4\left( \frac { dy }{ dx } \right) \)+y = 3ex

  6. Write down the order and degree of the following differential equations.
    \(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0

  7. Write down the order and degree of the following differential equations.
    \(\sqrt { 1+\left( \frac { dy }{ dx } \right) ^{ 2 } } \)= 4x

  8. Find the differential equation for y = mx + \(\frac { a }{ m } \) where m is arbitrary constant.

  9. Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

  10. Solve: x dy +y dx = 0

  11. Solve: (x2 - ay)dx = (ax-y2)dy

  12. The change in the cost of ordering and holding C as quantity q is given by \(\frac { dC }{ dq } =a-\frac { c }{ q } \) where a is a Constanst. Find C as a function of q.

  13. Solve: 3\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -5\frac { dy }{ dx } \)+ 2y = 0

  14. Solve: (D2-6D+25)y = 0

  15. Find the order and degree of the following differential equation
    \(y=2{ \left( \frac { dy }{ dx } \right) }^{ 2 }\)+ 4x\(\frac { dx }{ dy } \)

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