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#### Ordinary Differential Equations - Two Marks Study Materials

12th Standard EM

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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: $\frac{dy}{dx}+y=e^{-x}$