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

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.

straight x squared dy space equals space left parenthesis 2 xy plus straight y squared right parenthesis dx space space space rightwards double arrow dy over dx space equals space fraction numerator 2 xy plus straight y squared over denominator straight x squared end fraction space.... left parenthesis straight i right parenthesis space space space Let space straight y space equals space vx comma space space space space dy over dx equals straight v plus straight x dv over dx space space space Substituting space in space left parenthesis straight i right parenthesis comma space we space straight g space space space space space straight v plus straight x dv over dx space equals space fraction numerator 2 vx squared plus straight v squared straight x squared over denominator straight x squared end fraction space space rightwards double arrow space space straight v plus straight x dv over dx space equals space 2 straight v plus straight v squared space space space rightwards double arrow space straight x dv over dx equals space straight v squared plus straight v space space space rightwards double arrow space fraction numerator dv over denominator straight v squared plus straight v end fraction equals dx over straight x

Integrating both sides,

rightwards double arrow space integral fraction numerator dv over denominator straight v squared plus straight v end fraction equals integral dx over straight x rightwards double arrow integral fraction numerator straight v plus 1 minus straight v over denominator straight v left parenthesis straight v plus 1 right parenthesis end fraction. dv space equals space integral dx over straight x rightwards double arrow integral dv over straight v minus integral fraction numerator dv over denominator straight v plus 1 end fraction equals integral dx over straight x rightwards double arrow space logv minus log open vertical bar straight v plus 1 close vertical bar equals logx space plus space logC rightwards double arrow log open vertical bar fraction numerator straight v over denominator straight v plus 1 end fraction close vertical bar space equals space log open vertical bar Cx close vertical bar rightwards double arrow log open vertical bar fraction numerator begin display style bevelled straight y over straight x end style over denominator begin display style bevelled straight y over straight x end style plus 1 end fraction close vertical bar equals log open vertical bar Cx close vertical bar

rightwards double arrow space fraction numerator straight y over denominator straight y plus straight x end fraction equals Cx space left square bracket Removing space logarithm space in space both space sides right square bracket therefore space straight y equals Cxy plus Cx squared comma space which space is space the space general space solution. space Putting space straight y space equals space 1 space space and space straight x space equals space 1 comma 1 space equals space straight C space plus space straight C space space rightwards double arrow space space 2 straight C space equals space 1 space space space rightwards double arrow space straight C equals 1 half space space space straight y space equals space xy over 2 plus straight x squared over 2 space therefore 2 straight y space equals space xy plus straight y squared comma space which space is space the space particular space solution.

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