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Find the general solution of the given second-order differential equations

y +y=sinx 1.2 y +12y +36y =0,

y(0)=0,

y (0)=1,

y (0)=−7

User Jackrugile
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1 Answer

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Final answer:

The question is about solving a second-order differential equation, where the goal is to find its general solution and use given initial conditions to solve for unknown constants. Without a clear equation provided, a precise solution cannot be given, but typically one would solve the characteristic equation and use the initial conditions to find specific constants in the solution.

Step-by-step explanation:

The question provided seems to contain a mix of unrelated elements, but the fundamental inquiry is about finding the general solution of a given second-order differential equation. The equation provided seems to be of the form y'' + ay' + by = 0, where y is a function of x and the prime symbols denote derivatives with respect to x. Given this form, the general solution can be found using standard methods for solving linear homogeneous second-order differential equations, which often involve finding the roots of the characteristic equation r^2 + ar + b = 0 and then using these roots to construct the general solution.

Given specific initial conditions y(0)=0, y'(0)=1, and y''(0)=-7, one could substitute these into the general solution to solve for any unknown constants. Since the equation given seems to be missing or unclear, it is not possible to provide an exact solution. However, for a correct equation, solving for the constants would involve a bit of algebra after substituting the initial conditions into the general solution.

User Beasone
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