#### Differential Equations One Mark Question

12th Standard EM

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Time : 00:30:00 Hrs
Total Marks : 15
10 x 1 = 10
1. The degree of the differential equation $\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3$

(a)

1

(b)

2

(c)

3

(d)

4

2. The differential equation formed by eliminating a and b from y=ae+ be−x is

(a)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -y=0$

(b)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -\frac { dx }{ dy } =0$

(c)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0$

(d)

$\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -x=0$

3. The complementary function of (D2+ 4)y = e2x is

(a)

(Ax +B)e2x

(b)

(Ax +B)e−2x

(c)

A cos 2x + B sin 2x

(d)

Ae−2x+ Be2x

4. The differential equation of y = mx + c is (m and c are arbitrary constants)

(a)

$\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } }$ = 0

(b)

y = x $\frac { dy }{ dx }$ + c

(c)

xdy + ydx = 0

(d)

ydx − xdy = 0

5. The differential equation satisfied by all the straight lines in xy plane is

(a)

$\frac { dy }{ dx }$=a constant

(b)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$=0

(c)

y+ $\frac { dy }{ dx }$ = 0

(d)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$+y=0

6. If y = k.eλx then its differential equation where k is arbitrary constant is

(a)

$\frac { dy }{ dx }$=λy

(b)

$\frac { dy }{ dx }$=ky

(c)

$\frac { dy }{ dx }$+ky=0

(d)

$\frac { dy }{ dx }$=eλx

7. The differential equation obtained by eliminating a and b from y = a e3x + b e-3x is

(a)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$+ay=0

(b)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$-9y=0

(c)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } } -9\frac { dy }{ dx }$

(d)

$\frac { { d }^{ 2 }y }{ dx^{ 2 } }$+9x=0

8. The differential equation formed by eliminating A and B from y = ex (A cos x + B sin x) is

(a)

y2+y1=0

(b)

y2-y1=0

(c)

y2-2y1+2y=0

(d)

y2-2y1-2y=0

9. The degree of the differential equation $\sqrt { 1+\left( \frac { { d }y }{ dx } \right) ^{ \frac { 1 }{ 3 } } } =\frac { { d }^{ 2 }y }{ dx^{ 2 } }$ is

(a)

1

(b)

2

(c)

3

(d)

6

10. The degree of c =$\frac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 3 } \right] ^{ 2/3 } }{ \frac { d^{ 3 }y }{ dx^{ 3 } } }$ where c is a constant is

(a)

1

(b)

3

(c)

-2

(d)

2

11. 5 x 1 = 5
12. y= mx

13. (1)

1

14. Degree of linear differential equation

15. (2)

Family of lines

16. General form of linear equation

17. (3)

$\frac { dy }{ dx }$+Py=Q

18. I.F. of $\frac { dy }{ dx }$+Px=Q

19. (4)

$e^{ \int { pdy } }$

20. I.F. of $\frac { dy }{ dx }$+Py=Q

21. (5)

$e^{ \int { pdx } }$