(Solved): please help all of them! thank you Find the general solution of the differential equation r(t ...

please help all of them!

thank you

Find the general solution of the differential equation $${\mathbf{r}}^{?}(t)=(4?9t)\mathbf{i}+4t\mathbf{j}$$. (Use symbolic notation and fractions where needed. Give your answer in the form $$?x(t),y(t),z(t)?$$.) $$\mathbf{r}(t)$$ Find the solution with the initial condition $$\mathbf{r}(0)=2\mathbf{i}+4\mathbf{k}$$. (Use symbolic notation and fractions where needed. Give your answer in the form $$?x(t),y(t),z(t)?$$.) $$\mathbf{r}(t)$$ Compute the length of the curve $$\mathbf{r}(t)=?3t^2+1,6t^2?7,t^3?$$ over the interval $$0?t?2$$. (Use decimal notation. Give your answer to three decimal places.) $$S$$ Compute the arc length function $$s(t)={?}_a^t?{\mathbf{r}}^{?}(u)?du$$ for $$\begin{array}{rl}\mathbf{r}(t)& =?6\sqrt{2}{t}^{1/2},\ln (t),9t?\\ a& =1\end{array}$$ (Use symbolic notation and fractions where needed.) $$s=$$