What is expand y(d^2)/(d^2x)(y^2=x^2+2x) ?

The solution to expand y(d^2)/(d^2x)(y^2=x^2+2x) is (y^3)/x =x^2+2y

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expand y(d^2)/(d^2x)(y^2=x^2+2x)

expand

y \frac{d ^{2}}{d ^{2} x} (y^{2} = x^{2} + 2 x)

\frac{y ^{3}}{x} = x^{2} + 2 y

Solution steps

y \frac{d ^{2}}{d ^{2} x} (y^{2} = x^{2} + 2 x)

= \frac{d ^{2}}{d ^{2} x} y (= x^{2} y^{2} + 2 x)

Apply the distributive law:

a (b + c) = ab + a c

a = y \frac{d ^{2}}{d ^{2} x}, b = y^{2} = x^{2}, c = 2 x

y \frac{d ^{2}}{d ^{2} x} y^{2} = x^{2} + y \frac{d ^{2}}{d ^{2} x} \cdot 2 x

\frac{d ^{2}}{d ^{2} x} y y^{2} = x^{2} + 2 \cdot \frac{d ^{2}}{d ^{2} x} x y

Simplify

\frac{d ^{2}}{d ^{2} x} y y^{2} = x^{2} + 2 \cdot \frac{d ^{2}}{d ^{2} x} x y : \frac{y ^{3}}{x} = x^{2} + 2 y

\frac{y ^{3}}{x} = x^{2} + 2 y

(\frac{3 x}{4} - \frac{25}{4})^{2}

\frac{1}{( t ^{4} + 1 ) ^{3}}

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\frac{2 ( 715 - p ) ^{2}}{5}

What is expand y(d^2)/(d^2x)(y^2=x^2+2x) ?
The solution to expand y(d^2)/(d^2x)(y^2=x^2+2x) is (y^3)/x =x^2+2y