# Transient analysis with differential equation

Anyone may help with the differential equation for vC?

I write the Nodal analysis equations and find equation for vC but roots of characteristic equation is incorrect! v1 – the node where current source enters the top of schema

• The solution is already given on the image... What do you need actually? You only have to do the maths... Dec 23, 2016 at 11:30
• At first look the solution is shown previously but there is one mistake in it that I may not found - the result characteristic equation must be as in the next post! Dec 23, 2016 at 15:27

Kirchoff's voltage law: $$\large 20\int (3-i)dt+10(3-i)=4i+ 2\large\frac{di}{dt}$$

Differentiating: $$\large 60-20i-10\large\frac{di}{dt}=4\frac{di}{dt}+2\frac{d^2i}{dt^2}$$

Homogeneous equation is: $$\large p^2 + 7p + 10=0$$

• Thanks, when I use pure KVL and KCL I get equal characteristic equation, but when I'm using nodal analysis I do some magic mistake and can't get characteristic equation that you wrote. It's known that there is no difference what method of analysis to use (KVL, KCL, nodal, mesh current) the result must be same! May you help me to check error in my calculus? Dec 23, 2016 at 15:30
• You need to fill in the gaps in your analysis to find the error.
– Chu
Dec 23, 2016 at 16:32
• May you include some details? I can't understand about what you are talking. My vC equation - second row in matrix - don't have vC summand to achieve p^2 +7*p + 10 = 0 characteristic equation. Maybe some fact was lost in my nodal equations? Dec 24, 2016 at 14:56
• What books about circuit analysis may you recommend? Dec 24, 2016 at 14:57
• The matrix equations look ok, so show your steps to the characteristic equation
– Chu
Dec 24, 2016 at 15:28