x^{''}+9/4 x^'+9/64 x=0,x^'(0)=1,x(0)=2

Lösung

x^{^{''}} + \frac{9}{4} x^{^{'}} + \frac{9}{64} x = 0, x^{^{'}} (0) = 1, x (0) = 2

x = - \frac{( 32 - ( 13 2 - 12 ) ( 3 + 2 2 ) ) ( 3 + 2 2 ) e ^{\frac{3 ( 2 2 - 3 ) t}{8}}}{12} - \frac{13 2 - 12}{12} e^{- \frac{3 ( 3 + 2 2 ) t}{8}}

Schritte zur Lösung

x^{''} (t) + \frac{9}{4} x^{'} (t) + \frac{9}{64} x = 0

Solve linear ODE:

x = - \frac{( 32 - ( 13 2 - 12 ) ( 3 + 2 2 ) ) ( 3 + 2 2 ) e ^{\frac{3 ( 2 2 - 3 ) t}{8}}}{12} - \frac{13 2 - 12}{12} e^{- \frac{3 ( 3 + 2 2 ) t}{8}}

x = - \frac{( 32 - ( 13 2 - 12 ) ( 3 + 2 2 ) ) ( 3 + 2 2 ) e ^{\frac{3 ( 2 2 - 3 ) t}{8}}}{12} - \frac{13 2 - 12}{12} e^{- \frac{3 ( 3 + 2 2 ) t}{8}}

n = 0 \sum \infty \frac{1}{n ^{0.51}}

f (x) = 8 x + 9 3 x^{2} + 4 x^{3}

y \to \frac{1}{2} lim ((15 y^{2} - 6)^{4})

\int \frac{( x + 1 )}{4 x} d x

\int - \frac{3}{2} x d x