if dy/dx = 2 - x and f(2) = 1, use eulers method with 3 steps to approximate f(1.7)?\no a 1.3\no b 0.94\no c…

Explanation:

Step1: Calculate step - size

The initial point is $x_0 = 2$ and we want to get to $x = 1.7$ in $n = 3$ steps. The step - size $h=\frac{1.7 - 2}{3}=\frac{- 0.3}{3}=-0.1$.

Step2: First step of Euler's method

The formula for Euler's method is $y_{n+1}=y_n+h\cdot f'(x_n,y_n)$. Here $f'(x)=2 - x$, $x_0 = 2$, $y_0 = 1$. $y_1=y_0+h\cdot f'(x_0)$ $y_1 = 1+( - 0.1)\cdot(2 - 2)=1$. $x_1=x_0+h=2+( - 0.1)=1.9$.

Step3: Second step of Euler's method

$y_2=y_1+h\cdot f'(x_1)$ $f'(x_1)=2 - 1.9 = 0.1$. $y_2=1+( - 0.1)\cdot0.1=1 - 0.01 = 0.99$. $x_2=x_1+h=1.9+( - 0.1)=1.8$.

Step4: Third step of Euler's method

$y_3=y_2+h\cdot f'(x_2)$ $f'(x_2)=2 - 1.8 = 0.2$. $y_3=0.99+( - 0.1)\cdot0.2=0.99 - 0.02=0.97$.

Answer:

D. 0.97