Math Problem Statement
For the IVP
y′=x−y2, y(0)=−1,
the value of y(1) using Picard’s method after 2 approximations is
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Initial Value Problems
Numerical Methods
Picard's Method
Formulas
y_0(x) = y(0)
y_1(x) = -1 + ∫_0^x (t - 1) dt
y_2(x) = -1 + ∫_0^x (t - (y_1(t))^2) dt
Theorems
Picard's Theorem for Existence and Uniqueness of Solutions
Suitable Grade Level
Undergraduate (Mathematics)
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