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Beliebt Rechnen >

ay^{''}+by^'+cy=0

Lösung

a y^{^{''}} + b y^{^{'}} + cy = 0

Lösung

y = c_{1} e^{\frac{t ( - b + b ^{2} - 4 c a )}{2 a}} + c_{2} e^{\frac{t ( - b - b ^{2} - 4 c a )}{2 a}}

Schritte zur Lösung

a y^{''} (t) + b y^{'} (t) + cy = 0

Solve linear ODE:

y = c_{1} e^{\frac{t ( - b + b ^{2} - 4 c a )}{2 a}} + c_{2} e^{\frac{t ( - b - b ^{2} - 4 c a )}{2 a}}

y = c_{1} e^{\frac{t ( - b + b ^{2} - 4 c a )}{2 a}} + c_{2} e^{\frac{t ( - b - b ^{2} - 4 c a )}{2 a}}

Graph

Beliebte Beispiele

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

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

y^{''}+4y^'-5y=0,y(0)=1,y^'(0)=7

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = 7

(d^2y)/(dx^2)-8(dy)/(dx)+16y=0

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 16 y = 0

y^{'''}+4y^{''}+5y^'+2y=0

y^{^{'''}} + 4 y^{^{''}} + 5 y^{^{'}} + 2 y = 0

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

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