A C182 PILOT DEPARTED A CLASS D ARPT VFR BUT IMMEDIATELY AFTER TKOF BECAME IMC. ATIS INDICATED VFR BUT ACTUAL REQUIRED IFR.

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I WAS ATTEMPTING TO MOVE THE ACFT FROM ZZZ1 TO OUR HOME ARPT OF ZZZ2. WE HAD DIVERTED INTO ZZZ1 EARLY THAT MORNING DUE TO LOW CLOUDS/VISIBILITY AT OUR DEST. APPROX 4 HRS LATER THE ATIS SAID VIS 10 SM AND CEILING 1700 FT AGL; WHILE OUR DEST 25 MI AWAY WAS RPTING 10 SM AND CLR. I DETERMINED WE COULD SAFELY PROCEED AT 1700 FT MSL (1000 FT AGL) TO OUR DEST UNDER VFR. AFTER A NORMAL STARTUP; TAXI; AND RUNUP; WE ADVISED TWR WE WERE READY FOR DEP. TWR GAVE US A 140 DEG HDG AFTER DEPARTING RWY 23 AND MAINTAIN AT OR BELOW 3000 FT MSL. JUST BEFORE TKOF; I NOTICED LOWER CLOUDS IN THE DIRECTION OF MY VECTOR; BUT WAS IN SUCH A HURRY/RUSH TO GET HOME DUE TO FAMILY COMMITMENTS THAT I DIDN'T EVEN THINK TWICE ABOUT LAUNCHING AND JUST AVOIDING THOSE LOWER CLOUDS. UPON DEP; THE LOWER CLOUDS WERE AT APPROX 700 FT AGL AND WE WERE ALMOST IMMEDIATELY INTO THEM AFTER THE TURN TO 140 DEGS. THE LOWER LAYER WAS BTWN FEW AND SCATTERED; BUT I DEFINITELY VIOLATED THE CLASS D WX MINIMUMS ON CLOUD CLRNC AS I CLBED TO 1000 FT AGL. I THEN REQUESTED A LCL IFR TO JOIN THE APCH TO OUR DEST AND RECEIVED IT IN A VERY TIMELY MANNER FROM DEP. WE THEN JOINED THE APCH AND WERE CLR OF THE CLOUDS APPROX 5 MI LATER. I ALWAYS PREACH TO MY STUDENT THAT 'IF SOMETHING DOESN'T FEEL RIGHT; IT'S PROBABLY NOT.' I FELL INTO THE TRAP OF GET HOMEITIS AND SHOULD HAVE LISTENED TO MY EXPERIENCE AND FEELINGS ABOUT THE FLT. IN THE FUTURE; I WILL FORCE MYSELF TO SLOW DOWN AND REALLY EVALUATE THE WX SITUATION EVEN THOUGH I'M ONLY GOING SHORT DISTANCES. I HAD THE TOOL OF AN IFR AIRPLANE AND IFR EXPERIENCE; BUT DIDN'T USE THOSE TOOLS BECAUSE I WAS IN SUCH A HURRY.