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Beliebt Rechnen >

y^{''}+ay^'+by=0,y(0)=2cos(3x)

Lösung

y^{^{''}} + a y^{^{'}} + b y = 0, y (0) = 2 cos (3 x)

Lösung

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

Schritte zur Lösung

y^{''} (x) + a y^{'} (x) + b y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

y^{''}+2y^'+ay=0

y^{^{''}} + 2 y^{^{'}} + a y = 0

7y^{''}+y^'-y=0

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

y^{''''}+49y^{''}=0

y^{^{''''}} + 49 y^{^{''}} = 0

(d^2y)/(dx^2)-6(dy)/(dx)+25y=0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 25 y = 0