Solve the following differential equation dydx = x2y + y - Mathematics and Statistics

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Sum

Solve the following differential equation `("d"y)/("d"x)` = x2y + y

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Solution

`("d"y)/("d"x)` = x2y + y 

= (x2 + 1)y

∴ `1/y  "d"y` = (x2 + 1) dx

Integrating on both sides, we get

`int 1/y  "d"y = int(x^2 + 1)  "d"x`

∴ log |y| = `x^3/3 + x + c`

  Is there an error in this question or solution?
Chapter 1.8: Differential Equation and Applications - Q.4

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