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Beliebt Rechnen >

y^{''}-2y^'-3y=3te^{2t},y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = (- \frac{2}{3} + \frac{5}{3}) e^{3 t} + \frac{2}{3} e^{- t} - e^{2 t} t - \frac{2}{3} e^{2 t}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 3 y = 3 t e^{2 t}

Solve linear ODE:

y = (- \frac{2}{3} + \frac{5}{3}) e^{3 t} + \frac{2}{3} e^{- t} - e^{2 t} t - \frac{2}{3} e^{2 t}

y = (- \frac{2}{3} + \frac{5}{3}) e^{3 t} + \frac{2}{3} e^{- t} - e^{2 t} t - \frac{2}{3} e^{2 t}

Graph

Beliebte Beispiele

y^'=8x+y,y(0)=1

y^{^{'}} = 8 x + y, y (0) = 1

(dy)/(dx)=(2xy-y^2)/(x^2)

\frac{d y}{d x} = \frac{2 x y - y ^{2}}{x ^{2}}

(dy)/(dx)=(4x^3)/(cos(y))

\frac{d y}{d x} = \frac{4 x ^{3}}{cos ( y )}

derivative of (2x-1(3x+5))

\frac{d}{d x} ((2 x - 1) (3 x + 5))

limit as x approaches 2-of x^2+2

x \to 2 - lim (x^{2} + 2)