Exercises - Differential Equations

  1. Solve the following differential equations:

    1. $\displaystyle{x^2+4-y^3 \frac{dy}{dx} = 0}$

    2. $\displaystyle{\frac{dy}{dx} = \frac{5x^2y^2+y^2}{x^2y^5+4x^2}}$

    3. $\displaystyle{\frac{dy}{dx} = \frac{\csc^2 (2x) \cot (2x)}{4y}}$

    4. $\displaystyle{\cos x + 3y^2 \frac{dy}{dx} = 0}$

    5. $\displaystyle{\frac{dy}{dx} = \frac{y^2+x^2y^2}{3x^4+x^4y^2}}$

    6. $\displaystyle{\frac{\sqrt{x-4}}{y^2} = \frac{dy}{dx}}$

    7. $\displaystyle{\frac{x^2y(x^2+4)^2}{xy^2-xy^3} = \frac{dy}{dx}}$

    8. $\displaystyle{\frac{x+4}{\sqrt{xy}} = \frac{dy}{dx}}$

    9. $\displaystyle{x^2-5x+4 = \frac{dy}{dx}}$

    10. $\displaystyle{\frac{dy}{dx} = \frac{\sqrt{4-y} \cos \sqrt{x}}{y^2\sqrt{x}}}$

    11. $\displaystyle{\frac{dy}{dx} = \frac{x+4}{x^3 \csc (2y) \cot (2y)}}$