r^2y^{''}+y^'-n^2y=0

Lösung

r^{2} y^{^{''}} + y^{^{'}} - n^{2} y = 0

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

Schritte zur Lösung

r^{2} y^{''} (t) + y^{'} (t) - n^{2} y = 0

Solve linear ODE:

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

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

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

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y (1) = 5

0.05 y^{^{''}} + 2 y^{^{'}} + 100 y = 0

x^{^{''}} + \frac{0}{\frac{1}{32}} x^{^{'}} + \frac{13}{\frac{1}{32}} x = 0

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 5, y (0) = 6