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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = 0

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

y = c_{1} e^{2 x} + c_{2} x e^{2 x}

Graph

Beliebte Beispiele

y^{''}+9y=0,y(0)=1,y^'(0)=3

y^{^{''}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{''}-2y^'-8y=0,y(0)=α,y^'(0)=5

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = α, y^{^{'}} (0) = 5

y^{''}-3y^'+2y=0,y(0)=1,y^'(0)=2

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{'''}+4y^{''}-28y^'+32y=0

y^{^{'''}} + 4 y^{^{''}} - 28 y^{^{'}} + 32 y = 0

y^{'''}-9y^{''}=0

y^{^{'''}} - 9 y^{^{''}} = 0