Solve the initial value problem dy/dx=(x+y-1)^2 with y(0)=0 Solve the initial va

Question

Solve the initial value problem dy/dx=(x+y-1)^2 with y(0)=0

Solve the initial value problem dy/dx=(x+y-1)^2 with y(0)=0 Solve the initial value problem y' = (x+y-1)2 with y(0)= 0. a. To solve this, we should use this substitution u = u' = 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 linear differential equation in x, u, u'. c. The solution to the original initial value problem described by the following equation x, y.

Explanation / Answer

y'=(x+y-1)^2

a) put u = x+y-1

du/dx= 1+dy/dx

dy/dx= du/dx -1

b) du/dx-1= u^2

du/dx= 1+u^2

Integral 1/(1+u^2) du = Integral dx

arc tan u = x+c

u = tan(x+c)

C) put u= x+y-1

x+y-1= tan(x+c)

y= tan(x+c) +1-x

Given y(0)=0

0= tanc +1

c=arc tan(-1)

y=tan(x+ arc tan(-1)) +1 -x

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.