(d^4y)/(dx^4)+8(d^2y)/(dx^2)+6y=0

Lösung

\frac{d ^{4} y}{d x ^{4}} + 8 \frac{d ^{2} y}{d x ^{2}} + 6 y = 0

y = c_{1} cos (4 - 10 x) + c_{2} sin (4 - 10 x) + c_{3} cos (4 + 10 x) + c_{4} sin (4 + 10 x)

Schritte zur Lösung

\frac{d ^{4} y}{d x ^{4}} + 8 \frac{d ^{2} y}{d x ^{2}} + 6 y = 0

Solve linear ODE:

y = c_{1} cos (4 - 10 x) + c_{2} sin (4 - 10 x) + c_{3} cos (4 + 10 x) + c_{4} sin (4 + 10 x)

y = c_{1} cos (4 - 10 x) + c_{2} sin (4 - 10 x) + c_{3} cos (4 + 10 x) + c_{4} sin (4 + 10 x)

\frac{1}{2} x^{^{''}} + 3 x^{^{'}} + 4 x = 0, x (0) = 3, x^{^{'}} (0) = 0

y^{^{'''}} - 7 y^{^{''}} + 10 y = 0, y (0) = 7

y^{^{''}} + y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 1

l in e a r y^{^{''}} - y^{^{'}} = 0, y (0) = cos (x)

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = - 2, y^{^{'}} (0) = 2