Question

Find the equation of the curve from the given information:
a) dm/dt = 2t + 3, when t = 3 and m = 5

Answer 1

You can just integrate both sides to find the family of solutions. i.e.
\[m:=\int\frac{\textrm{d}m}{\textrm{d}t}\textrm{d}t=\int 2t+3 \textrm{d}t=t^2+3t+c,\quad c\in\mathbb{R}\]

Answer 2

the other side is 9 d5/d3

Answer 3

The you evaluate the initial condition, which states \[5=3^2+(3\times3)+c=18+c \Longrightarrow c=-13\Longrightarrow m=t^2+3t-13\]

Answer 4

wow is this 7th grade!!!