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Beliebt Rechnen >

y^{''}+αsqrt(2)y^'+2y=0

Lösung

y^{^{''}} + α 2 y^{^{'}} + 2 y = 0

Lösung

y = c_{1} e^{\frac{t ( - 2 α + 2 α ^{2} - 8 )}{2}} + c_{2} e^{\frac{t ( - 2 α - 2 α ^{2} - 8 )}{2}}

Schritte zur Lösung

y^{''} (t) + α 2 y^{'} (t) + 2 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t ( - 2 α + 2 α ^{2} - 8 )}{2}} + c_{2} e^{\frac{t ( - 2 α - 2 α ^{2} - 8 )}{2}}

y = c_{1} e^{\frac{t ( - 2 α + 2 α ^{2} - 8 )}{2}} + c_{2} e^{\frac{t ( - 2 α - 2 α ^{2} - 8 )}{2}}

Graph

Beliebte Beispiele

y^{''}-6y^'-2y=0,y(0)=1,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 1

(d^2y)/(dx^2)=-36y

\frac{d ^{2} y}{d x ^{2}} = - 36 y

y^{''}-6y^'+25y=0,y(0)=-3,y^'(0)=-1

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - 1

y^{''}+100/1 y^'=0

y^{^{''}} + \frac{100}{1} y^{^{'}} = 0

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

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