Final answer:
The student's question involves solving a linear ordinary differential equation with an initial condition, commonly taught in college-level mathematics courses.
Step-by-step explanation:
The question appears to be a differential equation problem: y' + 6y = e4t, with an initial condition y(0)=2.
This is typically associated with college-level mathematics, specifically within a course on differential equations or applied mathematics.
To solve this type of problem, we need to:
Identify the type of differential equation and check if it is linear and ordinary.
Use an integrating factor to solve the linear ordinary differential equation (ODE), or apply separation of variables if appropriate.
Apply the initial condition to find the particular solution to the ODE.
However, the specific steps to solve this equation are not provided within the given information, making it difficult to give a complete step-by-step solution.
Your correct question is: Use the Laplace transform to solve the given initial-value problem. y' + 6y = e4t, y(0) = 2 y(t) = Need Help? .Radltー!|Talk toa Tutor + -/1 points ZillDiffEQModAp 10 7.2.035 Use the Laplace transform to solve the given initial-value problem y" + 7y' + 6y = 0, y(0) = 1, y'(0) = 0 y(t)