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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)`
Solution
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)`.
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