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

98 Views

28. Show that the function y = ae^2X + be^–x is a solution of differential equation $fraction numerator straight d squared straight y over denominator dx squared end fraction minus dy over dx minus 2 straight y space equals space 0$ .

Here $straight y space equals space straight a space straight e to the power of 2 straight x end exponent plus straight b space straight e to the power of straight x$ ...(1)
$therefore space space space space dy over dx space equals space ae to the power of 2 straight x end exponent. space 2 space plus space straight b space straight e to the power of negative straight x end exponent left parenthesis negative 1 right parenthesis space space space space space space rightwards double arrow space space space space dy over dx space equals space 2 space straight a space straight e to the power of 2 straight x end exponent space minus space straight b space straight e to the power of negative straight x end exponent$ ...(2)
Again differentiating w.r.t. x, we get,
$fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 4 space straight a space straight e to the power of 2 straight x end exponent plus straight b space straight e to the power of straight x$ ...(3)
L.H.S. = $fraction numerator straight d squared straight y over denominator dx squared end fraction space minus dy over dx minus 2 straight y$
$equals space 4 space straight a space straight e to the power of 2 straight x end exponent plus space straight b space straight e to the power of straight x space minus space 2 space straight a space straight e to the power of 2 straight x end exponent plus space straight b space straight e to the power of negative straight x end exponent minus 2 space straight a space straight e to the power of 2 straight x end exponent minus space 2 space straight b space straight e to the power of negative straight x end exponent space space space space left square bracket because space of space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis comma space left parenthesis 3 right parenthesis right square bracket$
$equals space 0 space equals space straight R. straight H. straight S.$
$therefore space space space straight y space equals space straight a space straight e to the power of 2 straight x end exponent plus straight b space straight e to the power of straight x$ is a solution of the differential equation
$fraction numerator straight d squared straight y over denominator dx squared end fraction minus dy over dx minus 2 straight y space equals space 0$