Basic diff equations problem

**garymarkhov** · October 3rd 2009, 06:31 AM

Consider $\dot x = x+1$ . Find its solution x(t) satisfying the initial condition x(0)=0.

How should I attack this problem?

**TheEmptySet** · October 3rd 2009, 08:02 AM

Originally Posted by garymarkhov

Consider $\dot x = x+1$ . Find its solution x(t) satisfying the initial condition x(0)=0.

How should I attack this problem?

Remember that $\dot x =\frac{dx}{dt}$

This gives a first order seperable ODE.

$\frac{dx}{dt}=x+1 \iff \frac{dx}{x+1}=dt$

Integrating both sides we get

$\ln|x+1|=t+c$ solving for x gives

$x+1=Ae^{t} \iff x(t)=Ae^{t}-1$

From here just plug in your intial condition to find A.

Good luck.

**garymarkhov** · October 3rd 2009, 08:11 AM

Originally Posted by TheEmptySet

Remember that $\dot x =\frac{dx}{dt}$

This gives a first order seperable ODE.

$\frac{dx}{dt}=x+1 \iff \frac{dx}{x+1}=dt$

Integrating both sides we get

$\ln|x+1|=t+c$ solving for x gives

$x+1=Ae^{t} \iff x(t)=Ae^{t}-1$

From here just plug in your intial condition to find A.

Good luck.

Cool, so A = 1 and $x(t)=e^t$ right?