What is expand (x-1)^2y''(x)+(x-1)y'(x)-4y ?

The solution to expand (x-1)^2y''(x)+(x-1)y'(x)-4y is x^2y''(x)-2xy''(x)+y''(x)+xy'(x)-y'(x)-4y

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expand (x-1)^2y''(x)+(x-1)y'(x)-4y

expand

(x - 1)^{2} y^{''} (x) + (x - 1) y^{'} (x) - 4 y

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

Solution steps

(x - 1)^{2} y^{''} (x) + (x - 1) y^{'} (x) - 4 y

Expand

y^{'} (x) (x - 1) : x y^{'} (x) - y^{'} (x)

= (x - 1)^{2} y^{''} (x) + x y^{'} (x) - y^{'} (x) - 4 y

Simplify

(x - 1)^{2} y^{''} (x) + x y^{'} (x) - y^{'} (x) - 4 y : x^{2} y^{''} (x) - 2 x y^{''} (x) + y^{''} (x) + x y^{'} (x) - y^{'} (x) - 4 y

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

(x + 2)^{2}

\frac{2 ( s ^{2} - 5 )}{( s ^{2} + 1 ) ( s ^{2} + 25 )}

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

\frac{3}{( s - 10 ) ( s + 10 ) + a}

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

What is expand (x-1)^2y''(x)+(x-1)y'(x)-4y ?
The solution to expand (x-1)^2y''(x)+(x-1)y'(x)-4y is x^2y''(x)-2xy''(x)+y''(x)+xy'(x)-y'(x)-4y