2y^{''}+4y^'-7y=7cos(2x)

Lösung

2 y^{^{''}} + 4 y^{^{'}} - 7 y = 7 cos (2 x)

y = c_{1} e^{\frac{( - 2 + 3 ) x}{2}} + c_{2} e^{- \frac{( 2 + 3 ) x}{2}} + \frac{56}{289} sin (2 x) - \frac{105}{289} cos (2 x)

Schritte zur Lösung

2 y^{''} (x) + 4 y^{'} (x) - 7 y = 7 cos (2 x)

Solve linear ODE:

y = c_{1} e^{\frac{( - 2 + 3 ) x}{2}} + c_{2} e^{- \frac{( 2 + 3 ) x}{2}} + \frac{56}{289} sin (2 x) - \frac{105}{289} cos (2 x)

y = c_{1} e^{\frac{( - 2 + 3 ) x}{2}} + c_{2} e^{- \frac{( 2 + 3 ) x}{2}} + \frac{56}{289} sin (2 x) - \frac{105}{289} cos (2 x)

\int 1 + x d x

t an g e n t f (x) = e^{3 x}, at x = \frac{1}{3} ln (5)

\frac{d}{d x} (sin (x) ln (2 x))

\frac{d}{d x} (x \cdot e^{- 3 x})

\int \frac{cos ( θ )}{1 + sin ^{2} ( θ )} d θ