Electrical – Transient analysis with differential equation

differentialtransient

Anyone may help with the differential equation for vC?

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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

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Best Answer

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

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