Question

First verify that y(x) satisfies the given differential equation. Then determine a value of the constant C so that y(x) satisfies the given initial condition.

y′ = x − y;

y(x) = Ce−x + x − 1,

y(0) = 10.

Answer 1

Solution - The derivative of y(x) is:

y′(x) = −Ce^−x + 1.

We have,

So, the solution checks out. Solving for C we get:

So, the function y(x) that satisfies the differential equation and the given initial condition is:

y(x) = 11e^−x + x − 1.