Solution of IDZ Ryabushko 11.2 - Option 13

Section: Chapter 11. Ordinary Differential Equations
Topic: Differential Equations Allowing Order Reduction
Description: Finding the general and particular solutions of higher order differential equations allowing order reduction: equations of the type y^{(n)} = f(x), equations not explicitly containing the unknown function, equations not explicitly containing the independent variable. Also solving Cauchy problems and geometric problems leading to differential equations.

Tasks:
1. Find the particular solution of the differential equation and calculate the value of the resulting function y = φ(x) at x = x₀ accurate to two decimal places.
2. Find the general solution of the differential equation admitting order reduction.
3. Solve the Cauchy problem for a differential equation admitting order reduction.
4. Integrate the following equations.
5. Write the equation of a curve passing through point A(x₀, y₀), given that the slope of the tangent at any of its points equals the ordinate of that point multiplied by k.

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