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

Long Answer Type

261.

Find one-parameter families of solution curves of the following differential equation:
$left parenthesis 1 plus straight x squared right parenthesis space dy space plus space 2 xy space dx space equals space cot space straight x space dx space space space space left parenthesis straight x not equal to 0 right parenthesis$

75 Views

262.

Find one-parameter families of solution curves of the following differential equation:
$straight x dy over dx plus straight y minus straight x plus straight x space straight y space cot space straight x space equals space 0 space space space left parenthesis straight x not equal to 0 right parenthesis$

74 Views

263.

Solve: $open parentheses fraction numerator straight e to the power of negative 2 square root of straight x end exponent over denominator square root of straight x end fraction minus fraction numerator straight y over denominator square root of straight x end fraction close parentheses dx over dy equals 1 comma space space space straight x not equal to space 0.$

75 Views

264. Solve the following differential equation:

dy over dx space plus 2 space straight y space tan space straight x space equals space sin space straight x

79 Views

265. For the differential equation, find the general solution:

dy over dx plus 2 straight y space equals sin space straight x

74 Views

266. Solve the following differential equation:

sin space straight x space dy over dx plus straight y space cosx space equals space cos space straight x space sin squared straight x

73 Views

Short Answer Type

267. Find a one parameter family of solutions of each of the following differential equation:

straight y apostrophe cos squared straight x space equals space tanx minus space straight y

74 Views

268. Find a one parameter family of solutions of each of the following differential equation:

dy over dx equals negative fraction numerator straight x plus straight y space cosx over denominator 1 plus sinx end fraction

76 Views

Long Answer Type

269.

Solve:
$straight y apostrophe minus 2 straight y space equals space cos space 3 straight x$

71 Views

Short Answer Type

270.
Solve:
$straight y apostrophe plus straight y space equals space sin space straight x$

The given differential equation is $dy over dx plus straight y space equals space sin space straight x$
Comparing it with $dy over dx plus straight P space straight y space space equals straight Q comma space space we space get space comma space straight P space equals space 1 comma space straight Q equals space sin space straight x$
$therefore space space space space space space space integral straight P space dx space equals space integral 1 space dx space equals space straight x comma space space space space straight I. straight F. space equals space straight e to the power of integral straight P space dx end exponent space equals space straight e to the power of straight x$
$therefore space$ solution of differential equation is
$straight y. space straight e to the power of straight x space equals integral sinx. space straight e to the power of straight x space dx plus straight c space space space or space space space straight y. space straight e to the power of straight x space equals space fraction numerator 1 over denominator square root of 1 plus 1 end root end fraction straight e to the power of straight x sin space open parentheses straight x minus tan to the power of negative 1 end exponent 1 over 1 close parentheses plus straight c space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space integral straight e to the power of ax space sin space bx space equals space minus fraction numerator 1 over denominator square root of straight a squared plus straight b squared end root end fraction straight e to the power of ax space sin space open parentheses bx minus tan to the power of negative 1 end exponent straight b over straight a close parentheses close square brackets or space space space space straight y space equals fraction numerator 1 over denominator square root of 2 end fraction sin space open parentheses straight x minus straight pi over 4 close parentheses plus space ce to the power of negative straight x end exponent space space space space space space space$