Question

Solve the initial-value problem
y′′−4y=eˣ cosx , y(0)=0.7,y′(0)=−0.3.
u(x)=

Answer 1

The question asks for a solution to a non-homogeneous second-order differential equation with given initial conditions, which can be solved by finding a general and particular solution and applying initial values to determine constants.

Step-by-step explanation:

The subject of the question is to solve the initial-value problem given by the second-order differential equation y'' - 4y = e^x cos(x), with initial conditions y(0) = 0.7 and y'(0) = -0.3. This is a non-homogeneous differential equation that can be solved using methods such as undetermined coefficients or variation of parameters. While the specific steps to solve the equation are not provided, generally, one would first find the general solution to the associated homogeneous equation (where the right-hand side is zero) and then find a particular solution to the non-homogeneous equation. After finding the general solution, the initial conditions are used to determine the constants in the solution.