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Ordinary Differential Equations

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Please help solve #2.
Find the solution of the ODE: y'' + y = cot2t

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Step-by-step solutions to the ordinary differential equations are provided.

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Solutions to First-Order Ordinary Differential Equations

Question 1: (1 points)
Solve the following equations for given initial condition.

Please represent your answer in the implicit form ( ). Use y(x) instead of y
Question 2: (1 points)
Integrate the following equations and write a solution for given initial condition.

Please represent your answer in the implicit form ( ). Use y(x) instead of y.

Question 3: (1 points)
Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 4: (1 points)
Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 5: (1 points)
Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 6: (1 points)
Integrate the following equations and write a nontrivial solution.

Please represent your answer in the implicit form ( ). Use MAPLE syntax.

Question 7: (1 points)
Integrate the following equations and write a solution for given initial condition.

Please represent your answer in the explicit form ( ). Use MAPLE syntax. Use y(x) instead of y.

Question 8: (1 points)
Integrate the following equations and write a nontrivial solution.

Please represent your answer in the explicit form ( ). Use MAPLE syntax.

Question 9: (1 points)
Solve the following equation

Please represent your answer in the implicit form ( ), Use MAPLE syntax. Use y(x) instead of y.

Question 10: (1 points)
Make the change of variable for the homogenous differential equation

and find , where

Question 11: (1 points)
Solve the following equation

Please represent your answer in the explicit form ( ), Use MAPLE syntax. Use y(x) instead of y.

Question 12: (1 points)
Find the general solution of the linear differential equation (use C to denote a constant)
.

Question 13: (1 points)
Find the solution of the linear differential equation which satisfies the initial condition :
.

Question 14: (1 points)
Find the solution of the following differential equation:
.

Question 15: (1 points)
Solve the following equation for given initial condition

Please represent your answer in the explicit form ( ), Use MAPLE syntax. Use y(x) instead of y.

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