R1=0.1; R2=0.2;
L1=15; L2=5;
C=10;

A=[-R1/L1    0      -1/L1;
    0     -R2/L2    -1/L2;
    1/C     1/C       0];
[V D]=eig(A);
ICs=V(:,2)+V(:,3);
k=V\ICs;
s=@(t) k(1)*V(:,1)*exp(D(1,1)*t)...
      +k(2)*V(:,2)*exp(D(2,2)*t)...
      +k(3)*V(:,3)*exp(D(3,3)*t);
t=0:0.0001:100.0; % a vector of times
state=real(s(t));
plot(t,state(1,:),'r')
hold on
plot(t,state(2,:),'g')
plot(t,state(3,:),'m')
hold off