4y^{''}-12y^'+9y=0,y(1)=-2,y^'(-2)=-3

Lösung

4 y^{^{''}} - 12 y^{^{'}} + 9 y = 0, y (1) = - 2, y^{^{'}} (- 2) = - 3

y = \frac{2 ( - 3 e ^{\frac{9}{2}} - 4 ) e ^{\frac{3 t - 3}{2}}}{7} + \frac{( - 6 + 6 e ^{\frac{9}{2}} ) e ^{\frac{3 t - 3}{2}} t}{7}

Schritte zur Lösung

4 y^{''} (t) - 12 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = \frac{2 ( - 3 e ^{\frac{9}{2}} - 4 ) e ^{\frac{3 t - 3}{2}}}{7} + \frac{( - 6 + 6 e ^{\frac{9}{2}} ) e ^{\frac{3 t - 3}{2}} t}{7}

y = \frac{2 ( - 3 e ^{\frac{9}{2}} - 4 ) e ^{\frac{3 t - 3}{2}}}{7} + \frac{( - 6 + 6 e ^{\frac{9}{2}} ) e ^{\frac{3 t - 3}{2}} t}{7}

\int \frac{x}{1 + x ^{3}} d x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - y = 20 x e^{x}

\frac{d y}{d x} + y = x

n or ma l f (x) = 2 x^{2} - 5, (2, - 2)

\frac{d}{d x} (ln (x) + ln (sin (y)))