y^{'''}-ay^'=1+cosh(ax)

Lösung

y^{^{'''}} - a y^{^{'}} = 1 + cosh (a x)

y = c_{1} + c_{2} e^{a x} + c_{3} e^{- a x} - \frac{a x + sinh ( a x )}{a ^{2}} + e^{a x} \cdot \int \frac{e ^{- a x} ( cosh ( a x ) + 1 )}{2 a} d x + e^{- a x} \cdot \int \frac{e ^{a x} ( cosh ( a x ) + 1 )}{2 a} d x

Schritte zur Lösung

y^{'''} (x) - a y^{'} (x) = 1 + cosh (a x)

Solve linear ODE:

y = c_{1} + c_{2} e^{a x} + c_{3} e^{- a x} - \frac{a x + sinh ( a x )}{a ^{2}} + e^{a x} \cdot \int \frac{e ^{- a x} ( cosh ( a x ) + 1 )}{2 a} d x + e^{- a x} \cdot \int \frac{e ^{a x} ( cosh ( a x ) + 1 )}{2 a} d x

y = c_{1} + c_{2} e^{a x} + c_{3} e^{- a x} - \frac{a x + sinh ( a x )}{a ^{2}} + e^{a x} \cdot \int \frac{e ^{- a x} ( cosh ( a x ) + 1 )}{2 a} d x + e^{- a x} \cdot \int \frac{e ^{a x} ( cosh ( a x ) + 1 )}{2 a} d x

y^{^{''}} + 5 y^{^{'}} + 8 y = 24 + 23 x + 12 x^{2}

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} ln (x^{2} + 1)

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{2} e^{3}