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Beliebt Rechnen >

y^{''}-4y^'+4y=0,y^1(0)=e^{2x}

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y^{1} (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^{''}+4y^'+3y=0,y(0)=3,y^'(0)=-1

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 3, y^{^{'}} (0) = - 1

y^{'''}-5y^{''}+2y^'+8y=0

y^{^{'''}} - 5 y^{^{''}} + 2 y^{^{'}} + 8 y = 0

y^{''}-4y^'-3y=0

y^{^{''}} - 4 y^{^{'}} - 3 y = 0

y^{''}+9y^'+8y=0

y^{^{''}} + 9 y^{^{'}} + 8 y = 0

y^{^{''}} + k y^{^{'}} = 0