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Beliebt Rechnen >

y^{''}-3y^'+2y=(e^{3x})/(e^{2x)+1}

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{3 x}}{e ^{2 x} + 1}

Lösung

y = c_{1} e^{2 x} + c_{2} e^{x} + e^{2 x} arctan (e^{x}) - \frac{1}{2} e^{x} ln (e^{2 x} + 1)

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 2 y = \frac{e ^{3 x}}{e ^{2 x} + 1}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + e^{2 x} arctan (e^{x}) - \frac{1}{2} e^{x} ln (e^{2 x} + 1)

y = c_{1} e^{2 x} + c_{2} e^{x} + e^{2 x} arctan (e^{x}) - \frac{1}{2} e^{x} ln (e^{2 x} + 1)

Graph

Beliebte Beispiele

y^{''}+10000y=100sin(50x)

y^{^{''}} + 10000 y = 100 sin (50 x)

y^{''}+10y^'+15=0

y^{^{''}} + 10 y^{^{'}} + 15 = 0

(d^2x)/(dt^2)+(dx)/(dt)+x=1

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} + x = 1

y^{''}+y^'-y=t*e^t

y^{^{''}} + y^{^{'}} - y = t \cdot e^{t}

x^{''}+12x^'+11x=9cos(2t)

x^{^{''}} + 12 x^{^{'}} + 11 x = 9 cos (2 t)