For each of the differential equations in question, find the general solution:
y log y dx – x dy = 0

Question

For each of the differential equations in question, find the general solution: y log y dx – x dy = 0

Philoid · Accepted Answer

y log y dx – x dy = 0

⇒ (y log y) dx = xdy

Separating variables,

Integrating both sides,

⇒ let logy = t

⇒ log x + log c = log t

Or,

⇒ log x + log c = log (log y)

⇒ log cx = log y

Or,

⇒ log y = cx

For each of the differential equations in question, find the general solution:y log y dx – x dy = 0