(Solved): Section \( 7.1 \) Introduction First Order Systems: Problem 3 (1 point) Write the given second orde ...

Section \( 7.1 \) Introduction First Order Systems: Problem 3 (1 point) Write the given second order equation as its equivalent system of first order equations. \[ t^{2} u^{\prime \prime}+7 t u^{\prime}+\left(t^{2}+2.5\right) u=6 \sin (3 t) \] Use \( v \) to represent the "velocity function". i.e. \( v=u^{\prime}(t) \). Use \( v \) and \( u \) for the two functions, rather than \( u(t) \) and \( v(t) \). (The latter confuses webwork. Functions like sin \( (t) \) are ok.) \( u^{\prime}= \) \( v^{\prime}= \) Now write the system using matrices: Note: You can eam partial credit on this probiem.