Differential Equations Two Marks Question

12th Standard EM

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Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Form the differential equation by eliminating α and β from (x − α)2 + (y − β)2 = r2

2. Find the differential equation of the family of all straight lines passing through the origin.

3. Solve the following differential equations (D2+D−6)y=e3x + e−3x

4. Solve the following differential equations (D2−10D+25)y=4e5x + 5

5. Solve (D2-3D+2)y =e4x given y=0 when x=0 and x=1.

6. Find the order and degree of the following differential equations.
$\frac { d^{ 2 }y }{ { dx }^{ 2 } } =\sqrt { y-\frac { dy }{ dx } } =0$

7. Find the order and degree of the following differential equations.
${ \left( \frac { dy }{ dx } \right) }^{ 3 }+y=x-\frac { dx }{ dy }$

8. Solve: $\frac { a+{ x }^{ 2 } }{ 1+y } =xy\frac { dy }{ dx }$

9. Solve: $\frac { dy }{ dx }$ + ex+ye= 0

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

11. Write down the order and degree of the following differential equations.
$\left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 2 }{ 3 } }=\frac { d^{ 2 }y }{ { dx }^{ 2 } }$

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

13. Solve: x dy +y dx = 0

14. 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.

15. Solve: 3$\frac { { d }^{ 2 }y }{ dx^{ 2 } } -5\frac { dy }{ dx }$+2y=0