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.

Differential Equations

Short Answer Type

101. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:

straight e to the power of straight y dx plus straight e to the power of straight x dy space equals space 0

85 Views

102. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:
$left parenthesis sinx plus cosx right parenthesis space dy space equals space left parenthesis cosx minus sinx right parenthesis space dx$

The given differential equation is (sin x + cos x) dy = (cos x – sin x) dx

therefore space space space space space space space dy space equals space fraction numerator cosx minus sinx over denominator sinx plus cosx end fraction dx

Integrating,

integral 1 space dy space equals space integral fraction numerator cosx plus sinx over denominator sinx plus cosx end fraction dx

therefore space space space space space space space space space space space space space space space space space space straight y space equals log open vertical bar sinx plus cosx close vertical bar plus straight c comma space space space straight x space element of space straight R space is space the space solution

92 Views

103. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:

straight y apostrophe space equals left parenthesis 1 plus straight x squared right parenthesis thin space left parenthesis 1 plus straight y squared right parenthesis

88 Views

104. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:

left parenthesis straight e to the power of straight x plus straight e to the power of straight x right parenthesis space dy space minus space left parenthesis straight e to the power of straight x minus straight e to the power of straight x right parenthesis space dx space equals space 0

100 Views

105.

Solve the differential equation
$left parenthesis tan squared straight x plus 2 space tanx space plus 5 right parenthesis space dy over dx space equals space 2 left parenthesis 1 plus tanx right parenthesis space sec squared straight x.$