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Beliebt Rechnen >

y^{''}-2y^'+5y=2x^2+12

Lösung

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 x^{2} + 12

Lösung

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{2 x ^{2}}{5} + \frac{8 x}{25} + \frac{296}{125}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 5 y = 2 x^{2} + 12

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{2 x ^{2}}{5} + \frac{8 x}{25} + \frac{296}{125}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{2 x ^{2}}{5} + \frac{8 x}{25} + \frac{296}{125}

Graph

Beliebte Beispiele

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

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

y^{''}+y=-cos(2t),y(0)=0,y^'(0)=0

y^{^{''}} + y = - cos (2 t), y (0) = 0, y^{^{'}} (0) = 0

y^{''}+2y^'+5y=50xsin(x)+100xcos(x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 50 x sin (x) + 100 x cos (x)

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

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

y^{''}+9y=e^{2x}

y^{^{''}} + 9 y = e^{2 x}