16(d^4y)/(dx^4)+48(d^2y)/(dx^2)+36y=0

Lösung

16 \frac{d ^{4} y}{d x ^{4}} + 48 \frac{d ^{2} y}{d x ^{2}} + 36 y = 0

y = c_{1} cos (\frac{3}{2} x) + c_{2} sin (\frac{3}{2} x) + x (c_{3} cos (\frac{3}{2} x) + c_{4} sin (\frac{3}{2} x))

Schritte zur Lösung

16 \frac{d ^{4} y}{d x ^{4}} + 48 \frac{d ^{2} y}{d x ^{2}} + 36 y = 0

Solve linear ODE:

y = c_{1} cos (\frac{3}{2} x) + c_{2} sin (\frac{3}{2} x) + x (c_{3} cos (\frac{3}{2} x) + c_{4} sin (\frac{3}{2} x))

y = c_{1} cos (\frac{3}{2} x) + c_{2} sin (\frac{3}{2} x) + x (c_{3} cos (\frac{3}{2} x) + c_{4} sin (\frac{3}{2} x))

a re a x, x^{2} - 4 x + 3

d er i v a t i v e sin (x) ln (sec (x) + tan (x)) - 1

x \to 6 lim (\frac{x ^{2} - 5}{x - 6})

d er i v a t i v e f (x) = x^{2} 3 x + 5

d er i v a t i v e cos (a^{4} + x^{4})