Correcting Mistakes in Representing Constants for a Differential Equation?

[Jeff12341234]

I'm not sure if my answer is correct. Did I make a mistake somewhere? I'm not sure the ± needs to be there.

 

[HallsofIvy]

How in the world did you get a quadratic equation out of this? y(2)= (C_1+ 6C_2)e^6= e^6 and y'(1)= (3C_1+ 4C_2)e^3= e^3. The derivative is y'= 3C_1e^{3x}+ C_2e^{3x}+ 3C_2xe^{3x}= ([3C_1+ C_2]+ 3C_2x)e^x. It does not involve "C_1C_2"!

You have C_1+ 6C_2= 1 and 3C_1+ 4C_2= 1, two linear equations.

 

[Jeff12341234]

c1 is represented by c, c2 is represented by d

That's y'

I did make an error by leaving out the + sign between c1 and c2 for y'

That makes c1 = -1 and c2 = 1