${y}^{\u2033}=11-y$

$y(2)=1;{y}^{\prime}(2)=-4$

and asked to use Euler's method to find $y(2.2)$ for $h=0.1$

To find ${y}^{\prime}$ I simply took the integral of ${y}^{\u2033}$ to get:

${y}^{\prime}=11x-yx$

However, this does not satisfy the condition given above, that ${y}^{\prime}(2)=-4$. Is this not the correct way of obtaining the first order derivative?

$y(2)=1;{y}^{\prime}(2)=-4$

and asked to use Euler's method to find $y(2.2)$ for $h=0.1$

To find ${y}^{\prime}$ I simply took the integral of ${y}^{\u2033}$ to get:

${y}^{\prime}=11x-yx$

However, this does not satisfy the condition given above, that ${y}^{\prime}(2)=-4$. Is this not the correct way of obtaining the first order derivative?