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Beliebt Rechnen >

1/4 y^{''}+4y=tan(4t)-1/4 e^t

Lösung

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{4} e^{t}

Lösung

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 17 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 4 e ^{t} cos ^{2} ( 4 t ) - 4 e ^{t} sin ^{2} ( 4 t )}{68}

Schritte zur Lösung

\frac{1}{4} y^{''} (t) + 4 y = tan (4 t) - \frac{1}{4} e^{t}

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 17 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 4 e ^{t} cos ^{2} ( 4 t ) - 4 e ^{t} sin ^{2} ( 4 t )}{68}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 17 cos ( 4 t ) ln ( tan ( 4 t ) + sec ( 4 t ) ) - 4 e ^{t} cos ^{2} ( 4 t ) - 4 e ^{t} sin ^{2} ( 4 t )}{68}

Graph

Beliebte Beispiele

y^{''}+k^2y=sin(kx)

y^{^{''}} + k^{2} y = sin (k x)

(D^2-1)y=xe^{3x}

(D^{2} - 1) y = x e^{3 x}

y^{''}-2y^'+y=15e^x

y^{^{''}} - 2 y^{^{'}} + y = 15 e^{x}

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

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

D (x) = 72 - 1.8 x