Solve: from Mathematics Differential Equations

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.

Advertisement

Differential Equations

Short Answer Type

271.

Solve:
$dy over dx plus 2 straight y space equals space sin space 3 straight x$

73 Views

272.

Solve:
$dy over dx plus 2 straight y space equals space sin space 5 straight x$

74 Views

273.

Solve:
$dy over dx plus 2 straight y space equals space cos space 3 straight x$

73 Views

274.

Solve:
$dy over dx plus 3 straight y space equals space sin space 2 straight x$

74 Views

Advertisement

275.

Solve:
$dy over dx plus 3 straight y space equals space cos space 2 straight x$

79 Views

276.

Solve:
$dy over dx plus straight y space equals space cos space 2 straight x$

73 Views

277.

Solve:
$dy over dx plus straight y space secx space equals space tan space straight x$

76 Views

Advertisement

278.
Solve:
$dy over dx plus straight y space cotx space equals space straight x squared space cotx space plus space 2 straight x$

The given differential equation is

dy over dx plus straight y space cotx space equals straight x squared cotx space plus space 2 straight x

Comparing it with

dy over dx plus Py space equals space straight Q comma space space we space get comma

P = cot x,

straight Q space equals straight x squared space cot space straight x space plus space 2 straight x

integral straight P space dx space equals space integral cot space straight x space dx space equals space log space sinx. space straight e to the power of integral Pdx end exponent space equals space straight e to the power of log space sinx end exponent space equals space sin space straight x space

therefore

solution of differential equation is

straight y. space sin space straight x space equals space integral left parenthesis straight x squared space cot space straight x space plus space 2 straight x right parenthesis space sinx space dx space plus space straight c space space space space space open square brackets straight y space straight e to the power of integral Pdx end exponent space equals space integral straight Q space straight e to the power of integral straight P space dx end exponent dx plus straight c close square brackets

or

straight y. space sinx space space equals space integral left parenthesis straight x squared space cosx space plus 2 straight x space sin space straight x right parenthesis space dx space plus space straight c

or space space space straight y space sin space straight x space equals space integral space straight x squared space cosx space dx space space plus integral space 2 space straight x space sinx space dx space plus space straight c

or space space space straight y space sinx space minus straight x squared space sinx space minus space integral 2 straight x space sinx space dx space plus space integral 2 straight x space sinx space dx plus straight c or space space space straight y space sinx space space equals space straight x squared sin space straight x space plus space straight c

73 Views

Advertisement

Advertisement

279. Solve the differential equation:

left parenthesis 1 minus straight x squared right parenthesis space dy over dx plus straight x space straight y space equals space straight a space straight x

74 Views

Long Answer Type

280. Find the general solution of the following differential equation:

straight x dy over dx minus straight a space straight y space equals space straight x plus 1 comma space space space straight x greater than 0

78 Views

Advertisement