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Ordinary Differential Equations - Two Marks Study Materials

12th Standard EM

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. A differential equation, determine its order, degree (if exists)
    \(\frac { dy }{ dx } +xy=cotx\)

  2. A differential equation, determine its order, degree (if exists)
    \({ \left( \frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } \right) }^{ \frac { 2 }{ 3 } }-3\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +5\frac { dy }{ dx } +4=0\)

  3. A differential equation, determine its order, degree (if exists)
    \({ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0\)

  4. A differential equation, determine its order, degree (if exists)
    \({ \left( \frac { dy }{ dx } \right) }^{ 3 }=\sqrt { 1+\left( \frac { dy }{ dx } \right) } \)

  5. Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be-8x, where A and B are arbitrary constants.

  6. Find value of m so that the function y = emx is a solution of the given differential equation.
    y '+ 2y = 0

  7. Determine the order and degree (if exists) of the following differential equations: 
    \({ \left( \frac { { d }^{ 4 }y }{ { dx }^{ 4 } } \right) }^{ 3 }+4{ \left( \frac { dy }{ dx } \right) }^{ 7 }+6y=5cos3x\)

  8. Find the differential equation of the family of parabolas y2 ax = 4, where a is an arbitrary constant.

  9. Show that y=mx+\(\frac{7}{m}\),m≠0 is a solution of the differential equation xy'+7\(\frac{1}{y'}\)-y=0.

  10. Solve the Linear differential equation:
    \(\frac { dy }{ dx } =\frac { { sin }^{ 2 }x }{ 1+{ x }^{ 3 } } -\frac { { 3x }^{ 2 } }{ 1+{ x }^{ 3 } } y\)

  11. Form the differential equation satisfied by are the straight lines in my-plane.

  12. A curve passing through the origin has its slope ex, Find the equation of the curve.

  13. Solve: \(\frac{dy}{dx}=1+e^{x-y}\)

  14. Solve: x\(\frac{dy}{dx}=x+y\)

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

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