y^{'''}-y^'=tan(x)

Lösung

y^{^{'''}} - y^{^{'}} = tan (x)

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + ln (cos (x)) + e^{- x} \cdot \int \frac{e ^{x} tan ( x )}{2} d x + e^{x} \cdot \int \frac{e ^{- x} tan ( x )}{2} d x

Schritte zur Lösung

y^{'''} (x) - y^{'} (x) = tan (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + ln (cos (x)) + e^{- x} \cdot \int \frac{e ^{x} tan ( x )}{2} d x + e^{x} \cdot \int \frac{e ^{- x} tan ( x )}{2} d x

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + ln (cos (x)) + e^{- x} \cdot \int \frac{e ^{x} tan ( x )}{2} d x + e^{x} \cdot \int \frac{e ^{- x} tan ( x )}{2} d x

y^{^{''}} + 4 y^{^{'}} + 8 y = 12 e^{- 2 x} sec (2 x)

y^{^{''}} - 4 y = 20

y^{^{''}} + y = sinh (2 x)

y^{^{''}} + y^{^{'}} + 9.25 = 0

x^{^{''}} + 49 x = 65 cos (6 t)