SCALC8 9.5.024. My Notes A Bernoulli differential equation (named after James Bernoulli) is of the form dy dx + P(x)y = Q(x)yn. Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y1 − n transforms the Bernoulli equation into the linear equation du dx + (1 − n)P(x)u = (1 − n)Q(x). Use the substitution u = y1 − n to solve the differential equation. xy' + y = −5xy2

Divide through the ODE by the largest power of , assuming :

By the chain rule, . So substitute and to get

which is linear in . Multiply both sides by :

Now the left side is the derivative of a product, so we can condense this as

Integrate both sides with respect to :

Solve for :

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: