For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

Question

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation. x 2 = 2y 2 log y :

Philoid · Accepted Answer

It is given that x² = 2y² log y

Now, differentiating both sides w.r.t. x, we get,

2x = 2.

Now, substituting the value of in the LHS of the given differential equation, we get,

= xy –xy

= 0

Therefore, the given function is the solution of the corresponding differential equation.

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.x2 = 2y2 log y :

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
x² = 2y² log y :