2y^{'''}=e^xy^{'''}

Lösung

2 y^{^{'''}} = e^{x} y^{^{'''}}

y = \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

Schritte zur Lösung

2 y^{'''} (x) = e^{x} y^{'''} (x)

Isoliere

y^{'''} (x) : y^{'''} (x) = 0

Löse

y^{'''} (x) = 0 : y^{''} (x) = c_{1}

Löse

y^{''} (x) = c_{1} : y^{'} (x) = c_{1} x + c_{2}

Löse

y^{'} (x) = c_{1} x + c_{2} : y = \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

y = \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

f^{^{'}} (x) = 4 x + 9

2 y^{^{'}} + y^{3} = 0

2 x^{2} y^{^{'}} = x^{2} + y^{2}

x^{3} y^{^{'''}} - x^{2} y^{^{'}} = 0

5 x (x + 4 y) y^{^{'}} = 5 y (x - 4 y)