Question

A curve has the slope 2x+3 at each point (x,y) on the curve. What is an equation for this curve if it passes through the point (1,2)

Answer 1

I keep getting 2x^2+x-1 as my asnwer but the answer is y=x^2+3x-2

Answer 2

i used y-y1 = m(x-x1) and subsitited m with 2x+3 and the x and y with (1,2).

Answer 3

im not sure what im doing wrong

Answer 4

write down differentiatial eq with initial condition
y'=2x+3

y(1)=2

y=x^2+3x+C
2=1^2+3+C
2=4+C
C=-2

y= x^2+3x-2

Answer 5

to go from y' to y , I integrated it

Answer 6

oh ok. I see. I was doing something else completely different. This makes sense. Thanks. It was so easy and i cant belive i couldnt figure it out