Consider the differential equation $\frac { d y } { d x } = 2 x + y$ .(a) Sketch the direction field. Indicate where the slopes are $- 1$ , 0, or 1. Draw some other slopes as well.(b) If the point $( 1,2 )$ is on the graph of a solution, use Euler's Method with step size $0.5$ to estimate the value of the solution at $x = 2.5$ .

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The Answer of Consider the differential equation $\frac { d y } { d x } = 2 x + y$ .(a) Sketch the direction field. Indicate where the slopes are $- 1$ , 0, or 1. Draw some other slopes as well.(b) If the point $( 1,2 )$ is on the graph of a solution, use Euler's Method with step size $0.5$ to estimate the value of the solution at $x = 2.5$ .

Consider the Differential Equation dydx=2x+y\frac { d y } { d x } = 2 x + ydxdy​=2x+y

Consider the Differential Equation $\frac { d y } { d x } = 2 x + y$