(d^2y)/(dx^2)+3(dy)/(dx)+y=0

Lösung

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + y = 0

y = c_{1} e^{\frac{( - 3 + 5 ) x}{2}} + c_{2} e^{\frac{( - 3 - 5 ) x}{2}}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 5 ) x}{2}} + c_{2} e^{\frac{( - 3 - 5 ) x}{2}}

y = c_{1} e^{\frac{( - 3 + 5 ) x}{2}} + c_{2} e^{\frac{( - 3 - 5 ) x}{2}}

y^{^{''}} - 6 y^{^{'}} + 34 y = 0, y (0) = 5, y^{^{'}} (0) = - 5

y^{^{''}} - 10 y^{^{'}} + 50 y = 0, y (0) = - 4, y^{^{'}} (0) = - 5

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = e^{(\frac{2 x}{3})}

y^{^{''}} + 2 y^{^{'}} + (1 + \frac{9}{4} π^{2}) y = 0

y^{^{''}} + 16 y = 0, y (0) = cos (4 x)