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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{5}}{20}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{5}}{20}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{5}}{20}

Graph

Beliebte Beispiele

y^{''}+4y=-12sin(2x),y(0)=1.8,y^'(0)=5

y^{^{''}} + 4 y = - 12 sin (2 x), y (0) = 1.8, y^{^{'}} (0) = 5

y^{''}-11y^'+24y=13+24x

y^{^{''}} - 11 y^{^{'}} + 24 y = 13 + 24 x

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

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

y^{''}+y^'-2y=-260sin(3t)

y^{^{''}} + y^{^{'}} - 2 y = - 260 sin (3 t)

y^{''}-9y=81x^3

y^{^{''}} - 9 y = 81 x^{3}