3y^'-8y=e^{-pit^2},y(0)=a

Lösung

3 y^{^{'}} - 8 y = e^{- π t^{2}}, y (0) = a

y = e^{\frac{8 t}{3}} \cdot \int \frac{e ^{\frac{- 3 π t ^{2} - 8 t}{3}}}{3} d t

Schritte zur Lösung

3 y^{'} (t) - 8 y = e^{- π t^{2}}

Solve linear ODE:

y = e^{\frac{8 t}{3}} \cdot \int \frac{e ^{\frac{- 3 π t ^{2} - 8 t}{3}}}{3} d t

y = e^{\frac{8 t}{3}} \cdot \int \frac{e ^{\frac{- 3 π t ^{2} - 8 t}{3}}}{3} d t

\frac{d}{d x} (8 sin (3 x))

x \to \frac{+ π}{2} lim (4 sec (x))

d er i v a t i v e sin (x^{3})

x \to 0 lim (- 3 x^{3} - 7 x + 8)

d er i v a t i v e (2 x - 2)^{4} (x^{2} + x + 1)^{5}