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Mathematics : Differential Equations

Short Answer Type

211. Find a one parameter family of solutions of each of the following differential equation:
y² + x² y' = x y y'

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Long Answer Type

212. Find a one parameter family of solutions of each of the following differential equation:
(y² – 2xy) dx = (x² – 2xy) dy

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213. Find a one parameter family of solutions of each of the following differential equation:
y² dx + (x² – x y + y²) dy = 0

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214. Find a one parameter family of solutions of each of the following differential equation:
(x² + x y) dy = (x² + y²) dx

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215. Solve the following differential equation:

open parentheses 1 plus straight e to the power of straight x over straight y end exponent close parentheses space dx space plus space straight e to the power of straight x over straight y end exponent space open parentheses 1 minus straight x over straight y close parentheses dy space equals space 0

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Short Answer Type

216.

Solve $open parentheses straight x space sin space straight y over straight x close parentheses dy space equals open parentheses straight y space sin space straight y over straight x minus straight x close parentheses dx$

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Long Answer Type

217.

Show that the differential equation $straight x space cos space open parentheses straight y over straight x close parentheses dy over dx space equals straight y space cos space open parentheses straight y over straight x close parentheses plus straight x$ is homogeneous and solve it.

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218.

Show that the differential equation:
$left parenthesis straight x space dy space minus space straight y space dx right parenthesis space straight y space sin space open parentheses straight y over straight x close parentheses space equals space left parenthesis straight y space dx space plus space straight x space dy right parenthesis space straight x space cos space open parentheses straight y over straight x close parentheses$

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Short Answer Type

219.

Solve:
$straight y space straight e to the power of straight x over straight y end exponent dx space equals open parentheses xe to the power of straight x over straight y end exponent plus straight y squared close parentheses space space dy comma space space space straight y not equal to 0$

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220.

Solve:
$straight x dy over dx minus straight y plus straight x space tan straight y over straight x equals 0$

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