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#### Ordinary Differential Equations Model Question Paper 1

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

(a)

2

(b)

3

(c)

4

(d)

1

2. The solution of the differential equation 2x$\frac{dy}{dx}-y=3$represents

(a)

straight lines

(b)

circles

(c)

parabola

(d)

ellipse

3. If p and q are the order and degree of the differential equation $y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,$When

(a)

p < q

(b)

p = q

(c)

p>q

(d)

p exists and q does not exist

4. The solution of sec2x tan y dx+sec2y tan x dy=0 is

(a)

tan x+tan y =c

(b)

sec x+sec y=c

(c)

tan x tan y=c

(d)

sec x-sec y =c

5. The solution of (x2-ay)dx=(ax-y2)dy is

(a)

y=x2+y2-a(x+y)

(b)

y=x2+y2-a(x+y)

(c)

x3+y2=3ayx+c

(d)

(x2-ay)(ax-y2)=0

6. 5 x 2 = 10
7. A differential equation, determine its order, degree (if exists)
$\sqrt { \frac { dy }{ dx } } -4\frac { dy }{ dx } -7x=0$

8. A differential equation, determine its order, degree (if exists)
$y\left( \frac { dy }{ dx } \right) =\frac { x }{ \left( \frac { dy }{ dx } \right) +{ \left( \frac { dy }{ dx } \right) }^{ 3 } }$

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

10. Solve: $\frac{dy}{dx}=1+e^{x-y}$

11. Solve: $\frac{dy}{dx}+y=e^{-x}$

12. 5 x 3 = 15
13. Express the physical statement in the form of the differential equation.
A saving amount pays 8% interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuously at the rate of Rs 400 per year.

14. Find the differential equation of the family of all non-vertical lines in a plane.

15. Find the differential equation of the family of circles passing through the points (a,0) and (−a,0).

16. Form the differential equation for y=e-2x [A coos 3x-B sin 3x]

17. Solve: $\frac{dy}{dx}+y=cos x$

18. 4 x 5 = 20
19. Solve $\frac { dy }{ dx } =\frac { x-y+5 }{ 2(x-y)+7 } .$

20. Solve:$\frac { dy }{ dx }$ =(3x+y+4)2.

21. The surface area of a balloon being inflated changes at a constant rate. If initially, its radius 3 units and after 2 seconds it is 5 units, find the radius after t seconds.

22. Solve: $\frac { dy }{ dx }$ = (3x+2y+1)2