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

Question

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

Sum

Solution

`("d"y)/("d"x)` = x²y + y

∴ `("d"y)/("d"x)` = y(x² + 1)

∴ `("d"y)/y` = (x² + 1) dx

Integrating on both sides, we get

`int ("d"y)/y = int(x^2 + 1) "d"x`

∴ log |y| = `x^3/3 + x + "c"`

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Differential Equations

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Chapter 2.6: Differential Equations - Attempt the following questions II

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SCERT Maharashtra Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC

Chapter 2.6 Differential Equations
Attempt the following questions II | Q 6

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