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Beliebt Rechnen >

y^{''}+4y=2xe^{3x},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} + 4 y = 2 x e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = \frac{12}{169} cos (2 x) + \frac{5}{169} sin (2 x) + \frac{2 e ^{3 x} x}{13} - \frac{12}{169} e^{3 x}

Schritte zur Lösung

y^{''} (x) + 4 y = 2 x e^{3 x}

Solve linear ODE:

y = \frac{12}{169} cos (2 x) + \frac{5}{169} sin (2 x) + \frac{2 e ^{3 x} x}{13} - \frac{12}{169} e^{3 x}

y = \frac{12}{169} cos (2 x) + \frac{5}{169} sin (2 x) + \frac{2 e ^{3 x} x}{13} - \frac{12}{169} e^{3 x}

Graph

Beliebte Beispiele

y = 8 x^{2} - 6

f(x)= 2/4 x^5-1/3 x^3+3/6 x^2+1/2 x

f (x) = \frac{2}{4} x^{5} - \frac{1}{3} x^{3} + \frac{3}{6} x^{2} + \frac{1}{2} x

derivative of arcsin(x^6)

\frac{d}{d x} (arcsin (x^{6}))

2y^{''}+5y^'+3y=e^{-t}

2 y^{^{''}} + 5 y^{^{'}} + 3 y = e^{- t}

a y^{^{'}} + y = 0