What is expand (D^2-5){e^{5x}cos(2x)} ?

The solution to expand (D^2-5){e^{5x}cos(2x)} is D^2e^{5x}cos(2x)-5e^{5x}cos(2x)

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expand (D^2-5){e^{5x}cos(2x)}

expand

(D^{2} - 5) {e^{5 x} cos (2 x)}

D^{2} e^{5 x} cos (2 x) - 5 e^{5 x} cos (2 x)

Solution steps

(D^{2} - 5) {e^{5 x} cos (2 x)}

Apply the distributive law:

a (b - c) = ab - a c

a = {e^{5 x} cos (2 x)}, b = D^{2}, c = 5

= {e^{5 x} cos (2 x)} D^{2} - {e^{5 x} cos (2 x)} \cdot 5

= D^{2} {e^{5 x} cos (2 x)} - 5 {e^{5 x} cos (2 x)}

Remove parentheses:

(a) = a

= D^{2} e^{5 x} cos (2 x) - 5 e^{5 x} cos (2 x)

\frac{1}{2} sin (2 t) (\frac{7}{8} cos (4 t) + 3 (t + \frac{1}{4} sin (4 t)))

\frac{2 ( 1 + x )}{x ( x ^{2} + 4 )}

- 2 (- C (sin (x)) - D (cos (x)))^{2}

\frac{( 8 - x ) ^{2}}{4}

(4 x - \frac{1}{2})^{2}

What is expand (D^2-5){e^{5x}cos(2x)} ?
The solution to expand (D^2-5){e^{5x}cos(2x)} is D^2e^{5x}cos(2x)-5e^{5x}cos(2x)