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Beliebt Rechnen >

(d^2y)/(dx^2)=a^2y

Lösung

\frac{d ^{2} y}{d x ^{2}} = a^{2} y

Lösung

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} = a^{2} y

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{^{''}} + 6 y + 9 y = 0

linear y^{'''}-6y^{''}+12y^'-8y=0

l in e a r y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

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

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

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

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

10y^{''}+11y^'+3y=0

10 y^{^{''}} + 11 y^{^{'}} + 3 y = 0