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.

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

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

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

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

$straight y space equals space straight e to the power of negative 3 straight x end exponent$ ...(1)
$therefore$ $dy over dx space equals space straight e to the power of negative 3 straight x end exponent. space left parenthesis negative 3 right parenthesis space space space space space space space or space space space space space dy over dx equals negative 3 straight e to the power of negative 3 straight x end exponent$ ...(2)

$fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative 3 space straight e to the power of negative 3 straight x end exponent. space left parenthesis negative 3 right parenthesis space space space or space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 9 straight e to the power of negative 3 straight x end exponent$ ...(3)
L.H.S. = $fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 9 straight e to the power of negative 3 straight x end exponent minus 3 straight e to the power of 3 straight x end exponent minus 6 straight e to the power of negative 3 straight x end exponent space space space space space open square brackets because space of space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis comma space left parenthesis 3 right parenthesis close square brackets$
= 0 - R.H.S.
$therefore space space space straight y space equals straight e to the power of negative 3 straight x end exponent$ is a solution of the differential equation
$fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0$