Homogeneous Ordinary Differential Equations

Solve the following differential equations or Initial Value Problems (IVP).

  1. \(\displaystyle{\frac{dy}{dx} = \frac{y-x}{y+x}}\) View Solution
  2. \(\displaystyle{\frac{dy}{dx} = \frac{x^2+3y^2}{2xy}}\) View Solution
  3. \(\displaystyle{ -y \, dx + (x+\sqrt{xy})\, dy =0}\) View Solution
  4. \(\displaystyle{xy^2\frac{dy}{dx} = y^3-x^3, \quad y(1)=2}\) View Solution
  5. \(\displaystyle{(x^2+y^2)dx+(x^2-xy)dy =0 }\) View Solution
  6. \(\displaystyle{\frac{dy}{dx} = \frac{y-4x}{x-y}}\) View Solution