Solve t^2dt/dt=1-x

$$t ^ { 2 } \frac { d t } { d t } = 1 - x$$

Solve for x

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

Steps for Solving Linear Equation

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

$$1-x=t^{2}\frac{\mathrm{d}}{\mathrm{d}t}(t)$$

Subtract 1 from both sides.

$$-x=t^{2}\frac{\mathrm{d}}{\mathrm{d}t}(t)-1$$

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide t^{2}-1 by -1.

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

Solve for t

$$t=\sqrt{1-x}$$

$$t=-\sqrt{1-x}\text{, }x\leq 1$$