MthSc 208, Spring 2011 (Differential Equations)Dr. MacauleyHW 10Due Thursday March 3rd, 2011(1) Solve the following differential equations.(a)y0=-3y(b) 2y0=t+ 6y(c) 2y0=t2+ 6y(d)y00+ 4y= 0(e)y00=-9y+ 12.(2) For each system below, write it asAx=b. Find all solutions, and sketch the graph ofthe lines in each system on the same axis. Are the resulting lines intersecting, parallel, orcoincident?(a)x1+ 3x2= 0,2x1-x2= 0(b)-x1+ 2x2= 4,2x1-4x2=-6(c) 2x1-3x2= 4,x1+ 2x2=-5(d) 3x1-2x2= 0,-6x1+ 4x2= 0(e) 2x1-3x2= 6,-4x1+ 6x2=-12(3) For each part, find the determinant, eigenvalues and eigenvectors of the given matrix. Ifthe matrix is invertible, find its inverse.(a)A=3-22-2(b)A=3-24-1(c)
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