Question

Use Euler’s method with step size h = 0.1 to approximate y (1.2), where y(x) is a solution of the initial-value problem $\mathit{y}\mathbf{\text{'}}\mathbf{=}\mathbf{1}\mathbf{+}\mathit{x}\sqrt{\mathbf{y}}\mathbf{,}\mathit{y}\mathbf{\left(}\mathbf{1}\mathbf{\right)}\mathbf{=}\mathbf{9}$.

Short answer

The approximate value of y (1.2) is 9.8373.

Step-by-step solution

Note the given data

Given that step size h=0.1.

Consider the initial value problem $y\text{'}=1+x\sqrt{y},y\left(1\right)=9$.

Finding the required value

We use Euler’s method for finding the required value as follows:

$y_{n+1}=y_n+hf(x_n,y_n)$

Since, y (1) =9 and h= 0.1 , find y (1.1) as:

$\begin{array}{c}y(1.1)=9+0.1(1+1\times \sqrt{9})\\ =9.4\\ \approx y_1\end{array}$

Find the required value as follows: