(d^2y)/(dx^2)+100y=csc(10x)

Lösung

\frac{d ^{2} y}{d x ^{2}} + 100 y = csc (10 x)

y = c_{1} cos (10 x) + c_{2} sin (10 x) - \frac{1}{10} x cos (10 x) + \frac{1}{100} ln (sin (10 x)) sin (10 x)

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 100 y = csc (10 x)

Solve linear ODE:

y = c_{1} cos (10 x) + c_{2} sin (10 x) - \frac{1}{10} x cos (10 x) + \frac{1}{100} ln (sin (10 x)) sin (10 x)

y = c_{1} cos (10 x) + c_{2} sin (10 x) - \frac{1}{10} x cos (10 x) + \frac{1}{100} ln (sin (10 x)) sin (10 x)

y^{^{''}} + y^{^{'}} + y = x^{4} + 4 x^{3} + 12 x^{2}

(D^{2} + 5 D + 6) y = (D + 1) x

y^{^{''}} + 4 y^{^{'}} = 2 sec^{3} (2 t)

y^{^{''}} - 4 y^{^{'}} = 8 x^{2} + 2 e^{3 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = e^{- 2 x} + 3