ଯେକୌଣସି ଗଣିତ ସମସ୍ୟାକୁ ସମାଧାନ କରନ୍ତୁ

ପଦକ୍ଷେପ କ୍ରମେ

1. \frac{d^{2}}{d x^{2}} y{\left(x \right)} = -9.8

   The differential equation.

2. \text{order } 2

   Order 2: the highest derivative present.

3. \text{Undetermined coefficients}

   Solve the homogeneous part from the characteristic equation, then guess a particular solution shaped like the right-hand side.

4. r^{2} = 0

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

5. r = 0\ (\times 2)

   Its roots.

6. y{\left(x \right)} = C_{1} + C_{2} x - 4.9 x^{2}

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

7. \checkmark

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

ଉତ୍ତରକୁ ଖୋଲନ୍ତୁ

y{\left(x \right)} = C_{1} + C_{2} x - 4.9 x^{2}