4(d^2y)/(dx^2)+3(dy)/(dx)-10y=0

Lösung

4 \frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 10 y = 0

y = c_{1} e^{\frac{5 x}{4}} + c_{2} e^{- 2 x}

Schritte zur Lösung

4 \frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 10 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{5 x}{4}} + c_{2} e^{- 2 x}

y = c_{1} e^{\frac{5 x}{4}} + c_{2} e^{- 2 x}

(4 D^{2} - 4 D + 5) y = 0

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

\frac{1}{2} y^{^{''}} + 2 y = 0