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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

x^{''}+9x=0,x(0)=3,x^'(0)=4

x^{^{''}} + 9 x = 0, x (0) = 3, x^{^{'}} (0) = 4

y^{''}-7y^'+2y=0

y^{^{''}} - 7 y^{^{'}} + 2 y = 0

(d^2y)/(dt^2)+7(dy)/(dt)+ky=0

\frac{d ^{2} y}{d t ^{2}} + 7 \frac{d y}{d t} + k y = 0

solvefor x,(d^2x)/(dy^2)+0.1x=0

so l v e f or x, \frac{d ^{2} x}{d y ^{2}} + 0.1 x = 0

y^{''}-5y^'+6y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 1