What is expand ty''(t)+4(t-1)y'(t)+e^{2t}y ?

The solution to expand ty''(t)+4(t-1)y'(t)+e^{2t}y is ty''(t)+4ty'(t)-4y'(t)+e^{2t}y

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expand ty''(t)+4(t-1)y'(t)+e^{2t}y

expand

t y^{''} (t) + 4 (t - 1) y^{'} (t) + e^{2 t} y

t y'' (t) + 4 t y' (t) - 4 y' (t) + e^{2 t} y

Solution steps

t y^{''} (t) + 4 (t - 1) y^{'} (t) + e^{2 t} y

Expand

4 y^{'} (t) (t - 1) : 4 t y^{'} (t) - 4 y^{'} (t)

= t y^{''} (t) + 4 t y^{'} (t) - 4 y^{'} (t) + e^{2 t} y

(16 x - x^{2}) (4 + x)

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(x + 5) \cdot (x + 2)

(D^{2} - 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)))

What is expand ty''(t)+4(t-1)y'(t)+e^{2t}y ?
The solution to expand ty''(t)+4(t-1)y'(t)+e^{2t}y is ty''(t)+4ty'(t)-4y'(t)+e^{2t}y