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Differential-Equations · Differential-Equations

Y' = 1 + y^2

\frac{d}{d x} y{\left(x \right)} = y^{2}{\left(x \right)} + 1

Step by step

  1. \frac{d}{d x} y{\left(x \right)} = y^{2}{\left(x \right)} + 1

    The differential equation.

  2. \text{order } 1

    Order 1: the highest derivative present.

  3. \text{Separable}

    Move everything in y to one side with dy and everything in x to the other, then integrate both sides.

  4. y{\left(x \right)} = - \tan{\left(C_{1} - x \right)}

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

  5. \checkmark

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

Reveal the answer
y{\left(x \right)} = - \tan{\left(C_{1} - x \right)}