y^{''}+y^'=arctan(x)

Lösung

y^{^{''}} + y^{^{'}} = arctan (x)

y = c_{1} + c_{2} e^{- x} + x arctan (x) - \frac{1}{2} ln (x^{2} + 1) + e^{- x} \cdot \int - e^{x} arctan (x) d x

Schritte zur Lösung

y^{''} (x) + y^{'} (x) = arctan (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + x arctan (x) - \frac{1}{2} ln (x^{2} + 1) + e^{- x} \cdot \int - e^{x} arctan (x) d x

y = c_{1} + c_{2} e^{- x} + x arctan (x) - \frac{1}{2} ln (x^{2} + 1) + e^{- x} \cdot \int - e^{x} arctan (x) d x

y^{^{''}} + 2 y^{^{'}} - 8 y = 8 x^{2} - 3

\frac{d ^{2} y}{d x ^{2}} + y = - 16 \cdot cos (3 x)

(D - 2)^{2} y = 20 - 3 x e^{2} x

y^{^{''}} - y^{^{'}} - 15 = 0

y^{^{''}} - y^{^{'}} + 3 y = 9 t + 2