4. (Variation of parameters. ) You can check that r = 1 is a double root of the characteristic polynomial for y" - 2y' ty = e sin(2t). Use the method 'variation of parameters; to find the particularly solution. Solution: y(t) = Clet + C2tet _ e sin(2t) 4 5. Find the general solution of the Cauchy-Euler (or simply Euler) equation. x2y" + 3xy' + 10y = 0. Solution: First solve the indicial equation r(r - 1) + 3r + 10 =0. Then, we can get y (20 ) = 1 (C1 cos(3 log | | + C2 sin(3 log | |))