Can you help with 10 and 13?

Problem 10. (1 point) x ( t ) = Use the Laplace transform to solve the following initial value y O) = problem: Problem 11. (1 point) Find the Laplace transform of test sin (91). x' = 5x + 3y, y' =-2x+31 x(0) = 0, y(0) =0 Litest sin(90)}= Problem 12. (1 point) Find the Laplace transform of 12 sin(7t). Let X(s) = L{x(t) }, and Y(s) = Lty(t)}. L{12 sin(7t)} = _ V Find the expressions you obtain by taking the Laplace transform Problem 13. (1 point) of both differential equations and solving for Y (s) and X (s): Given that [ cos( 5V1) e-6.25/s X ( S) = Vit V's Y( s) = Find the partial fraction decomposition of X(s) and Y (s) and their find the Laplace transform of & cos(5VT). inverse Laplace transforms to find the solution of the system of DEs: I { VF cos ( 5 VF )) =