y^'=-5 x/2-2/5 x

Lösung

y^{^{'}} = - 5 \frac{x}{2} - \frac{2}{5} x

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

Schritte zur Lösung

y^{'} (x) = - 5 \frac{x}{2} - \frac{2}{5} x

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int - 5 \cdot \frac{x}{2} - \frac{2}{5} x d x

\int - 5 \cdot \frac{x}{2} - \frac{2}{5} x d x = - \frac{5 x ^{2}}{4} - \frac{x ^{2}}{5} + c_{1}

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

\frac{x ( 1 - x ) y ^{^{''}} - 5}{2 y ^{^{'}} - y} = 0

y^{^{''}} - 4 y + 4 y = 2 e^{2} x

f^{^{'}} (x) = \frac{2 cos ^{2} ( x )}{a ^{9}}

y^{^{''}} = 2 x + 1

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