(d^2y)/(dx^2)+2(dy)/(dx)=x

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 16 y = 3 csc^{2} (4 x)

y^{^{''}} - 4 y^{^{'}} + 3 y = (x^{2} - 3 x) e^{- x}

y^{^{''}} + y = 5

y^{^{''}} + y = 8

y^{^{''}} + 2 y = 4^{3} + 5 x^{2} - x + 7