4y^{''}-y=1,y^'(0)= 1/2 ,y(0)=0

Lösung

4 y^{^{''}} - y = 1, y^{^{'}} (0) = \frac{1}{2}, y (0) = 0

y = e^{\frac{t}{2}} - 1

Schritte zur Lösung

4 y^{''} (t) - y = 1

Solve linear ODE:

y = e^{\frac{t}{2}} - 1

y = e^{\frac{t}{2}} - 1

y^{^{''}} - y^{^{'}} - 20 = 0

\frac{d ^{2} y}{d x ^{2}} - 9 y = e^{3 x} cos (2 x) + e^{2 x}

y^{^{''}} + 9 y = cos (t)

y^{^{''}} + 4 y = t^{3} + 3 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

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