Answer Happy

The general solution of the homogeneous differential equation 2x²y" + 5xy + y = 0 can be written as Y₁ = ax¹ + bx¯¯ 2 where a, b are arbitrary constants and Yp = is a particular solution of the nonhomogeneous equation =3+5x 2x²y" +5xy + y = 30x + 3 By superposition, the general solution of the equation 2x²y + 5xy + y = 30x + 3 is y = y + Ур y = SO

NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 5, y (1) = 5 y = The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y₁ = x-¹ and y₂ = x-1/2 for the homogeneous equation is W =