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Question
Solve the differential equation
`y (dy)/(dx) + x` = 0
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Solution
Given differential equation is `y (dy)/(dx) + x` = 0
⇒ `y (dy)/(dx)` = – x
⇒ y dy = – x dx
On integrating both sides, we get
`int y dy = int - x dx`
⇒ `y^2/2 = (-x^2)/2 + C`
⇒ y2 + x2 = 2C
⇒ x2 + y2 = C
Where C = 2C is the required solution of differential equation.
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