Saved Bookmarks
| 1. |
\(\frac {d^4y}{dx^4} + \frac {d^3y}{dx^3} + \frac {d^2y}{dx^2}\) = 0d4y/dx4 + d3y/dx3 + d2y/dx2 = 0Homogeneous high order differential equation. |
|
Answer» Given differential equation is \(\frac {d^4y}{dx^4} + \frac {d^3y}{dx^3} + \frac {d^2y}{dx^2}\) It's auxiliary equation is m4 + m3 + m2 = 0 = m2 (m2+m+1) = 0 = m = 0, 0, \(\frac {-1\pm \sqrt{1-4}}{2}\) = m = 0, 0, \(\frac {-1}{2}\pm\frac {\sqrt3}{2}\) ∴ C.F. = (C1 + C2x)e0x + e-x/2 \((C_3\,cos\frac {\sqrt3}{2}x + C_4sin \frac {\sqrt3}{2}x)\) = C1 + C2 x + e-x/2 (\((C_3\, cos (\frac {\sqrt3}{2}x) + C_4\, sin (\frac {\sqrt3}{2}x)\) |
|