What is expand e^{2t}(e^ty+2e^ty'(t)+e^ty''(t)) ?

The solution to expand e^{2t}(e^ty+2e^ty'(t)+e^ty''(t)) is e^{3t}y+2e^{3t}y'(t)+e^{3t}y''(t)

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expand e^{2t}(e^ty+2e^ty'(t)+e^ty''(t))

expand

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

e^{3 t} y + 2 e^{3 t} y' (t) + e^{3 t} y'' (t)

Solution steps

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

Distribute parentheses

= e^{2 t} e^{t} y + e^{2 t} \cdot 2 e^{t} y^{^{'}} (t) + e^{2 t} e^{t} y^{^{''}} (t)

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

Simplify

e^{t} e^{2 t} y + 2 e^{t} e^{2 t} y^{'} (t) + e^{t} e^{2 t} y^{''} (t) : e^{3 t} y + 2 e^{3 t} y^{'} (t) + e^{3 t} y^{''} (t)

= e^{3 t} y + 2 e^{3 t} y^{'} (t) + e^{3 t} y^{''} (t)

(1 - y) e^{y} \frac{d y}{d x} + \frac{y ^{2}}{x ln ( x )}

\frac{( s + 2 ) e ^{- s}}{s ( s ^{2} + 4 s + 3 )}

\frac{1}{( 1 + x ) ^{3}}

(3 x - 2 y = 1, 1) (- 2 x + 2 y = - 8)

(1000000 x - 10000000) e^{0.001 x}

What is expand e^{2t}(e^ty+2e^ty'(t)+e^ty''(t)) ?
The solution to expand e^{2t}(e^ty+2e^ty'(t)+e^ty''(t)) is e^{3t}y+2e^{3t}y'(t)+e^{3t}y''(t)