y^{''}-1/2 y^'-1=0,y(0)=100,y(3)=10

Lösung

y^{^{''}} - \frac{1}{2} y^{^{'}} - 1 = 0, y (0) = 100, y (3) = 10

y = (100 - \frac{100 e ^{3} + 84 e ^{\frac{3}{2}} - 16}{e ^{3} - 1}) e^{\frac{t}{2}} + \frac{100 e ^{3} + 84 e ^{\frac{3}{2}} - 16}{e ^{3} - 1} - 2 t

Schritte zur Lösung

y^{''} (t) - \frac{1}{2} y^{'} (t) - 1 = 0

Solve linear ODE:

y = (100 - \frac{100 e ^{3} + 84 e ^{\frac{3}{2}} - 16}{e ^{3} - 1}) e^{\frac{t}{2}} + \frac{100 e ^{3} + 84 e ^{\frac{3}{2}} - 16}{e ^{3} - 1} - 2 t

y = (100 - \frac{100 e ^{3} + 84 e ^{\frac{3}{2}} - 16}{e ^{3} - 1}) e^{\frac{t}{2}} + \frac{100 e ^{3} + 84 e ^{\frac{3}{2}} - 16}{e ^{3} - 1} - 2 t

\frac{1}{2} y^{^{''}} + 2 y = 3 tan (2 t) - \frac{1}{2} e^{2 t}

y^{^{''}} + 4 y^{^{'}} + y = - 9

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 6

y^{^{''}} + y = 10

4 y^{^{''}} + y = e^{- 2 t} cos (\frac{t}{2}) + 6 t sin (\frac{t}{2})