In the following, verify that the given functions, (explicit or

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Advertisement

Differential Equations

Short Answer Type

21.

Determine the order and degree of the differential equation:
$square root of straight x fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus 5 open parentheses dy over dx close parentheses squared space equals 2 straight y squared minus straight x$

112 Views

Multiple Choice Questions

22. The degree of the differential equation

open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses cubed plus open parentheses dy over dx close parentheses squared plus sin open parentheses dy over dx close parentheses plus 1 space space equals space 0

is

3
2
1
1

95 Views

23. The degree of the differential equation

2 straight x squared fraction numerator straight d squared straight y over denominator dx squared end fraction minus 3 dy over dx plus straight y space equals space 0

is

2
1
0
0

99 Views

Short Answer Type

24. Verify that y = A cor x – B sin x is a solution of the differential equation

fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.

102 Views

Advertisement

25. Verify that the function y = a cos x + b sin x, where a, b ∊ R is a solution of the differential equation

fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.

95 Views

Long Answer Type

26. Verify that y - 3 cos (log x) + 4 sin (log x) is a solution of the differential equation

straight x squared fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x dy over dx plus straight y space equals space 0.

151 Views

Short Answer Type

27. Verify that the function y = e^–3x is a solution of the differential equation

fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0

98 Views

28. Show that the function y = ae^2X + be^–x is a solution of differential equation

fraction numerator straight d squared straight y over denominator dx squared end fraction minus dy over dx minus 2 straight y space equals space 0

.

94 Views

Advertisement

29. In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:

straight y space equals space straight e to the power of straight x plus 1

:

straight y to the power of straight n minus straight y apostrophe space equals space 0

128 Views

Advertisement

30. In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
$straight y space equals space straight x squared plus 2 straight x plus straight C$ : $straight y apostrophe minus 2 straight x minus 2 space equals space 0$

y = x² + 2 x + C
∴ y' = 2 x + 2
⇒ y' – 2 x – 2 = 0
∴ y = x² + 2 x + C is a solution of y' – 2 x – 2 = 0

97 Views

Advertisement

2
3
4

Advertisement