#### Differential Equations Book Back Questions

12th Standard EM

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
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 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

4. The integrating factor of x $\frac { dy }{ dx }$ - y = x2 is

(a)

$\frac {-1}{x}$

(b)

$\frac {1}{x}$

(c)

log x

(d)

x

5. The differential equation of x+ y= a2

(a)

xdy + ydx = 0

(b)

ydx – xdy = 0

(c)

xdx – ydx = 0

(d)

xdx + ydy = 0

6. 3 x 2 = 6
7. Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x axis.

8. Find the differential equation of the family of parabola with foci at the origin and axis along the x-axis.

9. Solve: (1 − x)dy − (1 + y)dx = 0

10. 3 x 3 = 9
11. Find the differential equation corresponding to y=ae4x + be−x where a, b are arbitrary constants.

12. Solve (D2−3D−4)y = 0

13. Solve : (D2−4D−1)y = e−3x

14. 2 x 5 = 10
15. The sum of Rs. 2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (loge2 = 0.6931)

16. Solve $\frac { dy }{ dx }$ −3ycotx=sin2x given that y = 2 when x = $\frac { \pi }{ 2 }$