Applying KCL to RC circuit and then solving DE for voltage
In case 2, you reversed the direction of the capacitor current.  Thus, the current is no longer given as CdV/dt but is now -CdV/dt. When you make that correction, the equation becomes the same as for case 1 and hence has the same solution, as it should. Remember, you can assign the current directions any way you want but then you must follow the circuit laws when calculating voltages.