Use the Laplace transform to solve the given system of differential equations. (d2x/dt2)+(d2y/dt2)=t2 (d2x/dt2)-(d2y/dt2)=6t x(0)=8,    x'(0)=0, y(0)=0,    y'(0)=0

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Consider the function of two variables  u (x,t) = 2e-t sin (2x)  Select the option that gives a partial differential equation for which this function of two variables is a solution.  A. (∂2u/∂x2) = 4(∂2u/∂t2)  B. (∂2u/∂x2) = (1/4)(∂2u/∂t2)  C. (∂2u/∂x2) = - (1/4)(∂2u/∂t2)  D. (∂2u/∂x2) = -4 (∂u/∂t)  E. (∂2u/∂x2) = 4 (∂u/∂t)

SOLVE STEP BY STEP IN DIGITAL FORMAT 9. Solve the differential equation (3xy + 2cos(y))dx + (x²-rsen(y))dy = 0 by integrating factor a)e-² (y²(x²y + 2sen(y)) - 1) = c b) (y(x²y + 2cos(y)) - 1) = c c) ³y + r²cos (y) = C