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Solve the equation : (dy)/(dx)=(x)/(y)

Solve the equation : dydx=xy \frac{d y}{d x}=\frac{x}{y}

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Full solution

Q. Solve the equation : dydx=xy \frac{d y}{d x}=\frac{x}{y}
  1. Multiply variables: Separate variables by multiplying both sides by yy and dxdx.y dy=x dxy \, dy = x \, dx
  2. Integrate both sides: Integrate both sides. ∫y dy=∫x dx\int y \, dy = \int x \, dx
  3. Perform integration: Perform the integration. y22=x22+C\frac{y^2}{2} = \frac{x^2}{2} + C, where CC is the constant of integration.
  4. Eliminate fractions: Multiply through by 22 to get rid of the fraction.y2=x2+2Cy^2 = x^2 + 2C
  5. Solve for CC: Solve for CC if initial conditions are given; if not, leave the answer in terms of CC.

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