Question

solve the initial value problem differential equation : dr/dt=(sec^2t)i+(4t^3+8)j initial condition r(0)=-8j

Answer 1

\[\int\limits_{}^{}dr = \int\limits_{}^{}\sec^{2} t+ 4t^{3}+8 dt\]
\[r = \tan t + t^{4}+8t + C\]
\[r(0) = 0+C = -8 \]
\[r= \tan t + t^{4}+8t -8\]