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Beliebt Rechnen >

y^{''}+y^'-6y=-e^{2x}+12x^2+2x+3

Lösung

y^{^{''}} + y^{^{'}} - 6 y = - e^{2 x} + 12 x^{2} + 2 x + 3

Lösung

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{e ^{2 x} x}{5} - 2 x^{2} - x - \frac{4}{3}

Schritte zur Lösung

y^{''} (x) + y^{'} (x) - 6 y = - e^{2 x} + 12 x^{2} + 2 x + 3

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{e ^{2 x} x}{5} - 2 x^{2} - x - \frac{4}{3}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{e ^{2 x} x}{5} - 2 x^{2} - x - \frac{4}{3}

Graph

Beliebte Beispiele

y^{''}+6y^'+25x=0

y^{''}-n^2y=(2cos(pin)x)/n

y^{''}+8y^'-2y= 5/(e^{3t)}

y^{''}+4y=sin(x),y(0)=0,y(1)=0