Question

The solution of the differential equation \(\frac{{dy}}{{dx}} + {y^2} = 0\) is
1. \(y = \frac{1}{{x + c}}\)
2. \(y = \frac{{ - {x^3}}}{3} + c\)
3. y = ce^x
4. unsolvable as the equation is non-linear

Answer 1

Correct Answer - Option 1 : \(y = \frac{1}{{x + c}}\)

Concept:

Variable separable:

Put all 'x' and 'y' terms separately on both sides of the equation.

Calculation:

Given:

\(\frac{{dy}}{{dx}} + {y^2} = 0\)

\(\frac{{dy}}{{y^2}} = -{dx} \)

\(\int\frac{{dy}}{{y^2}} = \int-{dx} \)

\(-\frac{1}{y}=-x+C\)

\(y=\frac{1}{x+c}\)