Question: Analytical Solution

This question explores the family of differential equations dy/dx=sqrt(􏰐 1 +􏰏( a*x )+ 􏰏 (2 *y)) for various values of the parameter a.  

For the case a = 􏰐 0 find the analytical solution that passes through the point (0, 1) and verify that this is a solution to the differential equation. Use this solution to find the value of y correct to 4 decimal placeswhen x=􏰐1. 

In maple i did

y:=(1/2)*x^2+sqrt(3)*x+1:
diff(y,x)
                             
i got the answer x + sqrt(3)

as shown in the markscheme. please cluld anyone help how to get y before this step and what to do after.

    

 

 

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