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

Multiple Choice Questions

301. The general solution of the differential equation e^x dy + (ye^x + 2x) dx = 0 is

x e^y + x² = C
x e^y + y² = C
y e^x + x² = C
y e^x + x² = C

78 Views

Short Answer Type

302.

Find the particular solution of the differential equation
$dy over dx equals negative fraction numerator x plus y space c o s space x over denominator 1 plus s i n space x space end fraction space g i v e n space t h a t space y equals 1 space w h e n space x equals 0$

1130 Views

303.

Find the particular solution of the differential equation

2ye^x/y dx+ (Y-2xe^x/y) dy =0

Given that x=0 when y=1.

761 Views

304.

Find the differential equation of the family of lines passing through the origin.

1357 Views

305.

If space straight y space equals space straight e to the power of ax. cosbx comma space then space prove space that space space space fraction numerator straight d squared straight y over denominator dx squared end fraction minus 2 straight a dy over dx plus left parenthesis straight a squared plus straight b squared right parenthesis straight y space equals space 0

516 Views

306.

If space straight x to the power of straight x plus straight x to the power of straight y plus straight y to the power of straight x space equals space straight a to the power of straight b comma space space then space find space dy over dx.

513 Views

307.
If $straight x equals straight a space sin space 2 straight t left parenthesis 1 plus cos space 2 straight t right parenthesis space and space straight y space equals straight b space cos space 2 straight t left parenthesis 1 minus cos space 2 straight t right parenthesis comma space then space find dy over dx space at space straight t space equals straight pi over 4.$

straight x equals straight a space sin space 2 straight t left parenthesis 1 plus cos space 2 straight t right parenthesis comma straight y equals space straight b space cos space 2 straight t left parenthesis 1 minus cos space 2 straight t right parenthesis dx over dt space equals 2 straight a space cos space 2 straight t left parenthesis 1 plus cos space 2 straight t right parenthesis space plus space straight a space sin space 2 straight t left parenthesis negative 2 space sin space 2 straight t right parenthesis space space space space equals space 2 straight a space cos 2 straight t space plus space 2 acos squared 2 straight t minus 2 straight a space sin squared 2 straight t space space space space equals 2 acos 2 straight t space plus space 2 acos 4 straight t space space space space dy over dt equals negative 2 bsin 2 straight t left parenthesis 1 minus cost space 2 straight t right parenthesis plus bcos 2 straight t left parenthesis 2 sin 2 straight t right parenthesis space space space space space space space equals space minus 2 bsin 2 straight t space plus 2 bsin space 2 tcos 2 straight t space plus 2 bcos 2 straight t space sin 2 straight t space space space space space space space equals negative 2 bsin 2 straight t plus 4 bsin 2 tcos 2 straight t space space space space space space space equals negative 2 bsin 2 straight t plus 2 bsin 4 straight t

fraction numerator begin display style dy over dt end style over denominator begin display style dx over dt end style end fraction equals fraction numerator negative 2 bsin 2 straight t plus 2 bsin 4 straight t over denominator 2 acos 2 straight t plus 2 acos 4 straight t end fraction space space space rightwards double arrow space space space dy over dx equals fraction numerator negative 2 bsin 2 straight t plus 2 bsin 4 straight t over denominator 2 acos 2 straight t plus 2 acos 4 straight t end fraction space space space space space rightwards double arrow space open vertical bar dy over dx close vertical bar subscript straight t equals straight pi over 4 end subscript space equals space fraction numerator negative 2 bsin begin display style fraction numerator 2 straight pi over denominator 4 end fraction end style plus 2 bsin begin display style fraction numerator 4 straight pi over denominator 4 end fraction end style over denominator 2 acos begin display style fraction numerator 2 straight pi over denominator 4 end fraction end style plus 2 acos begin display style fraction numerator 4 straight pi over denominator 4 end fraction end style end fraction space space space space space rightwards double arrow open vertical bar dy over dx close vertical bar subscript straight t equals straight pi over 4 end subscript space equals fraction numerator negative 2 bsin begin display style straight pi over 2 end style plus 2 bsinπ over denominator 2 acos begin display style straight pi over 2 end style plus 2 acosπ end fraction space space space space space rightwards double arrow open vertical bar dy over dx close vertical bar subscript straight t equals straight pi over 4 end subscript space equals fraction numerator negative 2 straight b over denominator negative 2 straight a end fraction equals straight b over straight a space space space space space space space space therefore space space space open vertical bar dy over dx close vertical bar subscript straight t equals straight pi over 4 end subscript space equals straight b over straight a space space space space space space space space space

783 Views

Long Answer Type

308.

Find the particulars solution of the differential equation $straight x squared dy space equals space left parenthesis 2 xy plus straight y squared right parenthesis dx comma space$ given that y =1 when x = 1.

438 Views

309.

Find the particulars solution of the differential equation $left parenthesis 1 plus straight x squared right parenthesis dy over dx equals open parentheses straight e to the power of straight m space tan to the power of negative 1 straight x end exponent end exponent minus straight y close parentheses comma space given space that space straight y space equals space 1 space when space straight x space equals space 0.$

315 Views

Short Answer Type

310.

Solve the differential equation $left parenthesis 1 plus straight x squared right parenthesis dy over dx plus straight y equals straight e to the power of tan to the power of negative 1 end exponent straight x end exponent$

132 Views

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

Short Answer Type

307. If

Long Answer Type

Short Answer Type