Mathematics II 4.6 Higher order linear equation with constant coefficent *Homogenous Example 1//Solve the equation d³y d4y d³y d²y dx5 - 3. +3 dx4 = 0 dx3 dx² Solution/ (D5-3D+3D3-D²)=0 D² (D3-3D² + 3D - 1) = 0 r² (33²+3r - 1) = 0 either r²=0r1 = r2 = 0 or (33r2+3r - 1) = 0 (r− 1)3 = 0 → r3 = r4 = r5 = 1 y=(c₁ex + c2 xe*x + c3e** + c4xe** + c5x²e**) → y=(c1ex + c2 xex + c3e1x + c4xetx +c5x2e1x) Exercise: Solve the equation d³y d²y +3 +3 dx3 dx² + y = 0 dx