Consider the vector field $\tilde{F}(x,y,z) = ax \tilde{i} + by \tilde{j} + cz\tilde{k}$
Let $\tilde{c}(t) = (x(t), y(t), z(t))$ be the flow line such that $\tilde{c}(0)= (x_0, y_0, z_0)$. Find $\tilde{c}(t)$ for all $t$.
I know that if $\tilde{c}(t)$ is a flow line then $\tilde{c}'(t) = \tilde{F}(\tilde{c}(t))$ but I have no idea what this question is actually asking for. Thanks in advance for any help/tips.