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Beliebt Rechnen >

y^{''}-4y^'=5e^{2x}-2cos(x)

Lösung

y^{^{''}} - 4 y^{^{'}} = 5 e^{2 x} - 2 cos (x)

Lösung

y = c_{1} e^{4 x} + c_{2} - \frac{5}{4} e^{2 x} + \frac{8}{17} sin (x) + \frac{2}{17} cos (x)

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) = 5 e^{2 x} - 2 cos (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} - \frac{5}{4} e^{2 x} + \frac{8}{17} sin (x) + \frac{2}{17} cos (x)

y = c_{1} e^{4 x} + c_{2} - \frac{5}{4} e^{2 x} + \frac{8}{17} sin (x) + \frac{2}{17} cos (x)

Graph

Beliebte Beispiele

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

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

4y^{''}-4y^'+y=72e^{t/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 72 e^{\frac{t}{2}}

y^{''}-y^'=4+e^x

y^{^{''}} - y^{^{'}} = 4 + e^{x}

(d^2y)/(dx^2)+(dy)/(dx)-6y=xe^{2x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = x e^{2 x}

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

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