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Beliebt Rechnen >

y^{''}+4y^'+5y=e^{2x}+1

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{2 x} + 1

Lösung

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{17} e^{2 x} + \frac{1}{5}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = e^{2 x} + 1

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{17} e^{2 x} + \frac{1}{5}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{17} e^{2 x} + \frac{1}{5}

Graph

Beliebte Beispiele

4y^{''}-y=e^{x/2}x

4 y^{^{''}} - y = e^{\frac{x}{2}} x

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

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

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

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

y^{''}-3y^'+5=e^{2x}-3cos(3x)

y^{^{''}} - 3 y^{^{'}} + 5 = e^{2 x} - 3 cos (3 x)

(D^2+D)(y)=sin(x)

(D^{2} + D) (y) = sin (x)