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Determine the solution x(t) for the following differential equations with the given initial conditions: a) 5x +10x=15 with x(0)=6 b) x +7x +10x=2 with x(0)=1; x (0)=0

User Decvalts
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Final answer:

We need to solve differential equations given specific initial conditions. The solution involves finding a function that satisfies both the differential equation and the initial conditions, and then verifying that the solution is correct.

Step-by-step explanation:

We are asked to find the solutions x(t) for two different differential equations with given initial conditions. The student has presented two separate parts of a calculus problem, both involving solving differential equations:

  • For part a) 5x +10x=15 with x(0)=6, we need to find a function x(t) whose derivative x'(t) and original function satisfy the equation.
  • For part b) x'' +7x' +10x=2 with x(0)=1; x'(0)=0, we first solve the characteristic equation related to the differential equation, then apply initial conditions to find the constants.

Both equations may be solved using characteristic polynomials and applying initial conditions; however, because the actual equations are missing certain details, we cannot provide a solution. It is important to verify the solution by substituting it back into the original differential equations and ensuring it satisfies the initial conditions provided.

User Gin Quin
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