Final answer:
The question appears to ask about solving a second order linear ordinary differential equation. However, the question does not contain a complete and correct equation to solve. We can use the quadratic formula to solve quadratic equations of the form ax² + bx + c = 0, where the solutions are given by the formula x = (-b ± √(b² - 4ac)) / (2a).
Step-by-step explanation:
The question refers to solving a differential equation of a particular form. The differential equation provided is a second order linear ordinary differential equation (ODE) with variable coefficients. The solution to such an equation is typically not straightforward and may require special functions or series solutions.
However, the query you have does not include a complete and intelligible differential equation, so solving it precisely as written is not possible. To confirm the proposed solution y=x^{p}(bx), one would usually substitute this expression into the original differential equation and show that it reduces to an identity. If you had a complete and correct differential equation, we could proceed with this verification.
The provided quadratic equations x² + 0.0211x - 0.0211 = 0 and similarly structured equations can be solved using the quadratic formula, which is applicable to any equation of the form ax² + bx + c = 0. The quadratic formula states that the solutions for x are given by x = (-b ± √(b² - 4ac)) / (2a). This formula would give the real or complex roots of the equation depending on the discriminant b² - 4ac.