||'''Book'''|| Advanced Engineering Mathematics ||
 ||'''Author'''|| Erwin Kreyszig ||
 ||'''Edition'''|| 8th Edition ||

/* code_begins */

{{{
R,L,C,E0,a,b,omega,k=var('R,L,C,E0,a,b,omega,k')
S=L*omega - 1/(omega*C)
I(t)=a*cos(omega*t)+b*sin(omega*t)
I(t)=I(t).subs(a=-(E0*S)/(R^2+S^2),b=(E0*R)/(R^2+S^2))
solve([L*k^2+R*k+1/C==0],k)
c1,c2,d1,d2=var('c1,c2,d1,d2')
I1 =c1*e^(d1*t)+c2*e^(d2*t)+ I(t)
I1(t) =I1.subs(d1=-1/2*(C*R + sqrt(C^2*R^2 - 4*C*L))/(C*L),d2=-1/2*(C*R - sqrt(C^2*R^2 - 4*C*L))/(C*L))
I2(t)=I1(t).subs(R=80,L=10,C=4/1000,E0=240.5,omega=10)
I3(t)=diff(I2(t),t)
print solve([I2(0)==0,
       I3(0)==0],c1,c2)
I2(t)=I(t).subs(R=80,L=10,C=4/1000,E0=240.5,omega=10)# since roots of the system of equations are imaginary. 
print 'I2(t) is'
print I2(t)
}}}

/* code_ends */

 * '''Solution by''': 
   * Hardik Gajera, student, IISER Pune
   * Lokesh Pimpale, student, IISER Pune