Question

Solve the initial value problem y′ =(x+y−4)² with y(0)=0. a. To solve this, we should use the substitution

u = x+t-4
u′ = 1+y'
Enter derivatives using prime notation (e.g., you would enter y′ for dy/dx)
b. After the substitution from the previous part, we obtain the following differential equation in x,u,u': ___________ c. The solution to the original initial value problem is described by the following equation in x,y. ______________

Answer 1

To solve the initial value problem y' =(x+y-4)² with y(0)=0, you can use the substitution u = x+y-4. After the substitution, the differential equation becomes u' = (u)². The solution to the original initial value problem is described by the equation y = x + u - 4.

Step-by-step explanation:

To solve the initial value problem y′ =(x+y−4)² with y(0)=0,

a. We can use the substitution u = x+y-4. Taking the derivative using prime notation, we get u′ = 1+y′.

b. After the substitution, the differential equation becomes u′ = (u)².

c. The solution to the original initial value problem is described by the equation y = x + u - 4.