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Differential-Equations · Differential-Equations

Dy/dx + y/x = 1

\frac{d}{d x} y{\left(x \right)} + \frac{y{\left(x \right)}}{x} = 1

Стъпка по стъпка

  1. \frac{d}{d x} y{\left(x \right)} + \frac{y{\left(x \right)}}{x} = 1

    The differential equation.

  2. \text{order } 1

    Order 1: the highest derivative present.

  3. \text{Exact}

    M dx + N dy = 0 with ∂M/∂y = ∂N/∂x: find the potential F with F_x = M, F_y = N; the solution is F = C.

  4. y{\left(x \right)} = \frac{C_{1}}{x} + \frac{x}{2}

    General solution (C₁, C₂ … are arbitrary constants).

  5. \checkmark

    Verified: substituting the solution back into the equation gives 0.

Разкрийте отговора
y{\left(x \right)} = \frac{C_{1}}{x} + \frac{x}{2}