y^{''}+3y^'-4y=10e^x-250cos(3x)

Lösung

y^{^{''}} + 3 y^{^{'}} - 4 y = 10 e^{x} - 250 cos (3 x)

y = c_{1} e^{x} + c_{2} e^{- 4 x} + 2 x e^{x} - 9 sin (3 x) + 13 cos (3 x)

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) - 4 y = 10 e^{x} - 250 cos (3 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 4 x} + 2 x e^{x} - 9 sin (3 x) + 13 cos (3 x)

y = c_{1} e^{x} + c_{2} e^{- 4 x} + 2 x e^{x} - 9 sin (3 x) + 13 cos (3 x)

n = 1 \sum \infty \frac{4 ^{n}}{n ^{4}}

\frac{d x}{d t} = - 3 x (\frac{1}{10} e^{- 2 t}), x (0) = \frac{4}{5}

\frac{\partial}{\partial y} (- 3 x^{2} + 7 x y - 4 y^{2} + x + y)

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}, y (1) = 6

\int \frac{1}{2} e^{2 t} d t