எந்த கணிதப் பிரச்சனையும் தீர்க்கவும்

படிப்படியாக

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

   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. r = 0

   Characteristic equation of the homogeneous part (substitute y = e^{rx}).

5. r = 0

   Its roots.

6. y{\left(x \right)} = C_{1} + \frac{x^{3}}{3}

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

7. \checkmark

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

விடை தெரியப்படுத்து

y{\left(x \right)} = C_{1} + \frac{x^{3}}{3}