(d^2y)/(dx^2)+9y=sin(3x)sec^2(3x)

Lösung

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x) sec^{2} (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- cos ( 3 x ) ( - 3 x + tan ( 3 x ) ) - ln ( cos ( 3 x ) ) sin ( 3 x )}{9}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x) sec^{2} (3 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- cos ( 3 x ) ( - 3 x + tan ( 3 x ) ) - ln ( cos ( 3 x ) ) sin ( 3 x )}{9}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- cos ( 3 x ) ( - 3 x + tan ( 3 x ) ) - ln ( cos ( 3 x ) ) sin ( 3 x )}{9}

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (t) - cos (2 t)

y^{^{''}} + 7 y^{^{'}} + 6 y = e^{2 t}

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- t}

y^{^{''}} - 2 y^{^{'}} + y = x + 1

y^{^{''}} + y = e^{- x} (2 sin (x) + 4 cos (x))