d x ( 4 x + 3 x ^ { 2 } ) = d y
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=\left(3x+4\right)x^{2}\end{matrix}\right.
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4dx^{2}+3dx^{3}=dy
Use the distributive property to multiply dx by 4x+3x^{2}.
4dx^{2}+3dx^{3}-dy=0
Subtract dy from both sides.
\left(4x^{2}+3x^{3}-y\right)d=0
Combine all terms containing d.
\left(3x^{3}+4x^{2}-y\right)d=0
The equation is in standard form.
d=0
Divide 0 by 3x^{3}+4x^{2}-y.
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