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Beliebt Rechnen >

(d^2y)/(dx^2)=ay+b

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+6y^'+5y=10cos(5t)

y^{^{''}} + 6 y^{^{'}} + 5 y = 10 cos (5 t)

y^{''}-4y^'-12y=sin(3t)

y^{^{''}} - 4 y^{^{'}} - 12 y = sin (3 t)

y^{''}+9y=sin(3x)+e^{2x}

y^{^{''}} + 9 y = sin (3 x) + e^{2 x}

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

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

y^{''}-2y^'-3y=2e^{3t}

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{3 t}