(d^2y)/(dx^2)=a(dy)/(dx)

Lösung

\frac{d ^{2} y}{d x ^{2}} = a \frac{d y}{d x}

y = c_{1} e^{a x} + c_{2}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} = a \frac{d y}{d x}

Solve linear ODE:

y = c_{1} e^{a x} + c_{2}

y = c_{1} e^{a x} + c_{2}

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

y^{^{''}} + 2 y^{^{'}} + 37 y = 0, y (0) = 2, y^{^{'}} (0) = - 26

y^{^{''}} - 4 y^{^{'}} + 29 y = 0, y (0) = 4, y^{^{'}} (0) = 18

y^{^{''}} - 83 y^{^{'}} + α y = 0

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