Solve r(t)=e^ti+e^2tj,quadt=0

$$r ( t ) = e ^ { t } i + e ^ { 2 t } j , \quad t = 0$$

Solve for r, t, j

$$r\in \mathrm{C}$$

$$t=0$$

$$j=-i$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$r\times 0=e^{0}i+e^{2\times 0}j$$

Anything times zero gives zero.

$$0=e^{0}i+e^{2\times 0}j$$

Calculate e to the power of 0 and get 1.

$$0=i+e^{2\times 0}j$$

Multiply 2 and 0 to get 0.

$$0=i+e^{0}j$$

Calculate e to the power of 0 and get 1.

$$0=i+1j$$

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

$$i+1j=0$$

Subtract i from both sides. Anything subtracted from zero gives its negation.

$$1j=-i$$

Divide both sides by 1.

$$j=\frac{-i}{1}$$

Divide -i by 1 to get -i.

$$j=-i$$

The system is now solved.

$$t=0 j=-i$$