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Beliebt Rechnen >

y^{''}-5y^'+6y=x^2+3x

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2} + 3 x

Lösung

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 6 y = x^{2} + 3 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

Graph

Beliebte Beispiele

y^{''}+3y^'=54x

y^{^{''}} + 3 y^{^{'}} = 54 x

(D^2+4D+5)y=50x+13e^{ex}

(D^{2} + 4 D + 5) y = 50 x + 13 e^{e x}

y^{''}-5y^'+6y=4e^{4x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 e^{4 x}

y^{''}+2y^'+3y=5sin(4t),y(0)=2,y^'(0)=1

y^{^{''}} + 2 y^{^{'}} + 3 y = 5 sin (4 t), y (0) = 2, y^{^{'}} (0) = 1

y^{''}-3y^'-4y=-16t,y(0)=-4,y^'(0)=-5

y^{^{''}} - 3 y^{^{'}} - 4 y = - 16 t, y (0) = - 4, y^{^{'}} (0) = - 5