The student didn't make any mistake. The slope of the line between those points is 3/8.
Answer:
6 2/6 in fractions or 6.3333.
The Bernoulli equation is almost identical to the standard linear ODE.

Compare to the basic linear ODE,

Meanwhile, the Riccati equation takes the form

which in special cases is of Bernoulli type if

, and linear if

. But in general each type takes a different method to solve. From now on, I'll abbreviate the coefficient functions as

for brevity.
For Bernoulli equations, the standard approach is to write


and substitute

. This makes

, so the ODE is rewritten as

and the equation is now linear in

.
The Riccati equation, on the other hand, requires a different substitution. Set

, so that

. Then you have



Next, setting

, so that

, allows you to write this as a linear second-order equation. You have



where

and

.
f(x) = 2x + 1 and g(x) = f(x) + 3
g(x) = 2x + 1 + 3
<h2><u>g(x) = 2x + 4</u></h2>
Answer:
I belive it is 3x^2 + x. Sometimes I'm braindead so it may be wrong.