Question

The solution of the differential equation `x "dt"/"dx" + 2y` = x² is ______.

Options

• y = `(x^2 + "c")/(4x^2)`

• y = `x^2/4 + "c"`

• y = `(x^4 + "c")/x^2`

• y = `(x^4 + "c")/(4x^2)`

Answer 1

The solution of the differential equation `x "dt"/"dx" + 2y` = x² is y = `(x^4 + "c")/(4x^2)`.

Explanation:

I.F. = `"e"^(int 2/x  "d"x) = "e"^(2logx)`

= `"e"^(logx^2)`

= x².

Therefore, the solution is y.

x² = `int x^2 * x "d"x`

= `x^4/4 + "k"`,

i.e., y = `(x^4 + "c")/(4x^2)`.