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Beliebt Rechnen >

y^{''}+y^'=y

Lösung

y^{^{''}} + y^{^{'}} = y

Lösung

y = c_{1} e^{\frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( - 1 - 5 ) t}{2}}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) = y

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( - 1 - 5 ) t}{2}}

y = c_{1} e^{\frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( - 1 - 5 ) t}{2}}

Graph

Beliebte Beispiele

y^{'''}+2y^{''}-19y^'-20y=0

y^{^{'''}} + 2 y^{^{''}} - 19 y^{^{'}} - 20 y = 0

(d^2y)/(dx^2)-6(dy)/(dx)+14y=0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 14 y = 0

y^{''}-13y^'+30y=0

y^{^{''}} - 13 y^{^{'}} + 30 y = 0

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

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

2y^{''}+5y^'-3y=0,y(0)=-1,y^'(0)=17

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 1, y^{^{'}} (0) = 17