a^2(d^2y)/(dx^2)+a(dy)/(dx)-c*y=0

Lösung

a^{2} \cdot \frac{d ^{2} y}{d x ^{2}} + a \cdot \frac{d y}{d x} - c \cdot y = 0

y = c_{1} e^{\frac{x ( - 1 + 4 c + 1 )}{2 a}} + c_{2} e^{- \frac{x ( 4 c + 1 + 1 )}{2 a}}

Schritte zur Lösung

a^{2} \cdot \frac{d ^{2} y}{d x ^{2}} + a \cdot \frac{d y}{d x} - c \cdot y = 0

Solve linear ODE:

y = c_{1} e^{\frac{x ( - 1 + 4 c + 1 )}{2 a}} + c_{2} e^{- \frac{x ( 4 c + 1 + 1 )}{2 a}}

y = c_{1} e^{\frac{x ( - 1 + 4 c + 1 )}{2 a}} + c_{2} e^{- \frac{x ( 4 c + 1 + 1 )}{2 a}}

y^{^{''''}} + 8 y^{^{''}} - 4 y^{^{'''}} - 16 y^{^{'}} + 16 y = 0

10 y^{^{''}} + 30 y^{^{'}} + 20 y = 0

\frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 49 y = 0

\frac{d ^{4} y}{d x ^{4}} - 4 y = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 5