Solve (a)y=x^2-siny

$$( a ) y = x ^ { 2 } - \sin y$$

Solve for a

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

Steps for Solving Linear Equation

The equation is in standard form.

$$ya=-\sin(y)+x^{2}$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{-\sin(y)+x^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{-\sin(y)+x^{2}}{y}$$

Solve for x

$$x=\sqrt{\sin(y)+ay}$$

$$x=-\sqrt{\sin(y)+ay}\text{, }\left(y\leq 0\text{ or }a\geq -\frac{\sin(y)}{y}\right)\text{ and }\left(y\geq 0\text{ or }a\leq -\frac{\sin(y)}{y}\right)$$