Solve y=ax^2+bx^3

$$y = a x ^ { 2 } + b x ^ { 3 }$$

Solve for a

$$\left\{\begin{matrix}a=-bx+\frac{y}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx^{3}=y$$

Subtract bx^{3} from both sides.

$$ax^{2}=y-bx^{3}$$

Reorder the terms.

$$ax^{2}=-bx^{3}+y$$

The equation is in standard form.

$$x^{2}a=y-bx^{3}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{y-bx^{3}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{y-bx^{3}}{x^{2}}$$

Divide y-bx^{3} by x^{2}.

$$a=-bx+\frac{y}{x^{2}}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{y-ax^{2}}{x^{3}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx^{3}=y$$

Subtract ax^{2} from both sides.

$$bx^{3}=y-ax^{2}$$

Reorder the terms.

$$bx^{3}=-ax^{2}+y$$

The equation is in standard form.

$$x^{3}b=y-ax^{2}$$

Divide both sides by x^{3}.

$$\frac{x^{3}b}{x^{3}}=\frac{y-ax^{2}}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$b=\frac{y-ax^{2}}{x^{3}}$$

Divide y-ax^{2} by x^{3}.

$$b=-\frac{a}{x}+\frac{y}{x^{3}}$$