Not as simple as it appears

Calculus Level 5

$\large \begin{cases} \dfrac{dv}{dt} = 4v - 5w \\ \dfrac{dw}{dt} = 2v - 3w \end{cases}$

Solve the system of differential equations above. Given that $v(0) = 8$ and $w(0) = 5$ , evaluate $\left \lfloor v(1) - w(1) \right \rfloor$

2 solutions

Fiki Akbar
Feb 27, 2015

By substracting the two original equations, we have $\frac{d}{dt} (v-w) = 2(v-w)$

Integrating the equation, we get the general solution $(v-w)(t) = C e^{2t}$

Since $(v-w)(0)=3$ , then $(v-w)(t) = 3e^{2t}$

For $t=1$ , we have $(v-w)(1) = 3e^{2} = 22.167$

Mayank Singh
Oct 21, 2015

Well, the title should be "It's simpler than it appears"

Absolutely correct

Prithwish Mukherjee - 2 years ago