y^{''}-y=x^2e^x+5

Lösung

y^{^{''}} - y = x^{2} e^{x} + 5

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 5

Schritte zur Lösung

y^{''} (x) - y = x^{2} e^{x} + 5

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 5

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} + \frac{- e ^{x} x ^{2} + e ^{x} x}{4} - 5

in v erse l a pl a ce \frac{5 s}{9 + s ^{2}}

d er i v a t i v e \frac{5 x ^{3} + 3 x ^{2}}{x}

\frac{\partial}{\partial x} (x^{2} (1 - y^{\frac{2}{5}}))

d er i v a t i v e y = x + x^{\frac{3}{2}} - 8 x

(5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y = 0