What is expand x^2(x+3)y''(x)-4(x+3)y'(x)-9xy ?

The solution to expand x^2(x+3)y''(x)-4(x+3)y'(x)-9xy is x^3y''(x)+3x^2y''(x)-4xy'(x)-12y'(x)-9xy

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expand x^2(x+3)y''(x)-4(x+3)y'(x)-9xy

expand

x^{2} (x + 3) y^{''} (x) - 4 (x + 3) y^{'} (x) - 9 x y

x^{3} y'' (x) + 3 x^{2} y'' (x) - 4 x y' (x) - 12 y' (x) - 9 x y

Solution steps

x^{2} (x + 3) y^{''} (x) - 4 (x + 3) y^{'} (x) - 9 x y

Expand

x^{2} y^{''} (x) (x + 3) : x^{3} y^{''} (x) + 3 x^{2} y^{''} (x)

= x^{3} y^{''} (x) + 3 x^{2} y^{''} (x) - 4 (x + 3) y^{'} (x) - 9 x y

Expand

- 4 y^{'} (x) (x + 3) : - 4 x y^{'} (x) - 12 y^{'} (x)

= x^{3} y^{''} (x) + 3 x^{2} y^{''} (x) - 4 x y^{'} (x) - 12 y^{'} (x) - 9 x y

\frac{4 x ^{2} ( 9 x ^{2} + 2 ) ^{2}}{( 1 + 4 x ^{2} + 9 x ^{4} ) ^{3}}

\frac{\partial}{\partial y} ((z) (e^{x z} + x y))

a (- 2, - \frac{π}{3})

\frac{10 x ^{2} + 7 x - 42}{( x - 2 ) ( x + 4 ) ( x - 1 )}

\frac{d}{d x} ((z) (sin (y z) - x - 2 y - 3 z))

What is expand x^2(x+3)y''(x)-4(x+3)y'(x)-9xy ?
The solution to expand x^2(x+3)y''(x)-4(x+3)y'(x)-9xy is x^3y''(x)+3x^2y''(x)-4xy'(x)-12y'(x)-9xy