Confused about solving RC circuits with nodal analysis

[timnswede]

Problem is in the picture below.

The problem is already solved, but I am confused as to why C(dv/dt) is positive and not negative, since the current is coming out of the capacitor and towards the point v(t), which is not away from v(t) like the solution shows. But if I solve the problem with the negative sign there I get an infinite voltage which obviously makes no sense. Can someone explain why we assume it's going away, unlike what would be done if it was a given current source?

 

[gneill]

In nodal analysis when one sums the currents and sets the result to zero, the sum is either that all currents are assumed to be coming into the node, or that all currents are leaving the node. There's no mix of directions.

In this case the assumption is that all currents are leaving the node, as can be verified by the terms for the resistors. So the assumed current direction is from the v(t) node to the capacitor.

 

[timnswede]

In nodal analysis when one sums the currents and sets the result to zero, the sum is either that all currents are assumed to be coming into the node, or that all currents are leaving the node. There's no mix of directions.

In this case the assumption is that all currents are leaving the node, as can be verified by the terms for the resistors. So the assumed current direction is from the v(t) node to the capacitor.

OK, that makes sense, thank you for clarifying.