Word Count : 361

---

To solve the initial value problem \( y' = x - y \) with \( y(0) = 1 \) at \( x = 0.1 \) using the third-order Taylor’s series method, we follow these steps: --- ### Step 1: Write the Taylor series expansion up to the third order The Taylor series expansion for \( y(x + h) \) is: \[ y(x + h) = y(x) + h y'(x) + \frac{h^2}{2!} y''(x) + \frac{h^3}{3!} y'''(x) + \cdots \] We need to compute \( y(0.1) \) using \( h = 0.1 ________ ________ ______ __________ ________.
________ _________ _________ _________ _________ ______ _________ ___ _______ ___ ____ ___.
_______ _________ ______ _______ _______ _________.
_________ ________ _______ ________ __________ ______ __________ ___.
____ ____ ____ ____ ___ ___.
_________ _______ ______ _____ ___ _________.
_________ ___ ___ ___ ___ ________.
______ ____ ___ ___ _____ ____ __________ _________ _______.
_______ ______ ____ _____ ___ ________ ________ ______ _______ ___ ________.
________ _______ _______ ____ _____ __________ __________ ___ ___ ____ ________ _____.
_______ ____ _____ ___ _____ ________ ____ ________ ___.
___ ________ _________ ______ __________ __________.
________ ____ __________ ________ _______.
______ _______ ___ _______ __________ __________ _______.
__________ ___ __________ ________ _____ _________.
______ ____ __________ __________ ____ _______.
__________ ____ ______ ___ ________.
___ _____ ____ ________ _________ __________ ______ _________.
__________ _________ ________ ___ _____ _______ ___ _____.
______ ____ ____ _________ _________ ____ _______ ________ __________ __________.
_____ _________ _________ ______ ___ _____ _________.
___ ________ _______ ____ ________ ________ ____ ______ _______ ___.
_______ __________ ____ ________ ______ ______ _________ ______ _______ ____ ___ ____.
___ _________ ____ ___ _________ _________ ________.
__________ _____ ____ ___ _________ __________ ______ __________ _____ ___.
_______ __________ _____ _______ _____ _____ ____ _______ ________ __________ _________.
___ _________ _____ _______ ___ _________ _____ ____ ___.
__________ __________ ______ ________ _______ _________ ________ _____ _________ __________ ____ __________.
________ _____ ________ _____ ___ ________ ____ _____ _________ __________ ________ _________.
_________ ________ __________ _____ ______ ___ _____ ___ _________ ________ _____.
___ ___ ___ _________ _____ ____ _________ ______ _______ _____.
______ ______ __________ ________ _____ _____ _____ ____ __________.
Get Full Answer on WhatsApp