Solve x^prime=2y+x^2

$$x ^ { \prime } = 2 y + x ^ { 2 }$$

Solve for y

$$y=\frac{1-x^{2}}{2}$$

Steps for Solving Linear Equation

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

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

Subtract x^{2} from both sides.

$$2y=\frac{\mathrm{d}}{\mathrm{d}x}(x)-x^{2}$$

The equation is in standard form.

$$2y=1-x^{2}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{1-x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{1-x^{2}}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{1-2y}$$

$$x=\sqrt{1-2y}$$

Solve for x

$$x=\sqrt{1-2y}$$

$$x=-\sqrt{1-2y}\text{, }y\leq \frac{1}{2}$$