y^{'''}+2x*x=0

Lösung

y^{^{'''}} + 2 x \cdot x = 0

y = - \frac{x ^{5}}{30} + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

Schritte zur Lösung

y^{'''} (x) + 2 x \cdot x = 0

Isoliere

y^{'''} (x) : y^{'''} (x) = - 2 x^{2}

Löse

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

Löse

y^{''} (x) = - \frac{2 x ^{3}}{3} + c_{1} : y^{'} (x) = - \frac{x ^{4}}{6} + c_{1} x + c_{2}

Löse

y^{'} (x) = - \frac{x ^{4}}{6} + c_{1} x + c_{2} : y = - \frac{x ^{5}}{30} + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

y = - \frac{x ^{5}}{30} + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

\int \frac{x ^{5} + x ^{4} - 8}{x ^{3} - 4 x} d x

\int x^{2} (x + 1)^{2} d x

\int ((x + \frac{1}{x})^{2} (x - \frac{1}{x})^{2} - x + \frac{1}{x}) d x

d er i v a t i v e 5 x^{2} y

x \to 0 lim (\frac{7 x ^{3} - x ^{2}}{x})