dsolve

Robert Israel — Wed, 17 Mar 2010 18:41:35 Z

Your equations are second order in both v[ds] and v[gs], so you need two more initial conditions to determine the solution uniquely. That's why there are still two arbitrary constants in the solution.

> eqns := 1.00011000*10^(-7)*(diff(v[gs](t), t))-1.000*10^(-12)
    *(diff(v[ds](t), t))+v[gs](t)+1.000*10^(-18)*(diff(v[gs](t), t, t))
    +5.00*10^(-19)*(diff(v[ds](t), t, t)) = 12, 2.900*10^(-18)*
    (diff(v[ds](t), t, t))+5.00*10^(-7)*(diff(v[gs](t), t))+6.00*10^(-19)
    *(diff(v[gs](t), t, t))+v[ds](t) = 24;
  ics:= v[gs](0) = 3.5, 
      v[ds](0) = `#msub(mi("V"),mo("in",fontweight = "bold"))`,
      D(v[gs])(0)= a, D(v[ds])(0)=b;

  dsolve({eqns, ics});

To evaluate the RootOfs numerically, you can use evalf.

> evalf(%);

The result is rather complicated, but that's life.

tks very much,Robert Israel !

andy.zhou.nuaa — Thu, 18 Mar 2010 04:46:55 Z

tks very much,Robert Israel !

simplification

Robert Israel — Wed, 17 Mar 2010 20:53:00 Z

Actually, we can simplify it somewhat.

> normal(fnormal(%));

{v[ds](t) = .4958026528*exp((30764029.75+1577330139.*I)*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`+9.149694069*exp((30764029.75+1577330139.*I)*t)-(.766755745*I)*exp((30764029.75+1577330139.*I)*t)-(0.3290893603e-1*I)*exp((30764029.75+1577330139.*I)*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`-0.3002643e-3*exp(-10002901.82*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`-42.51993430*exp(-10002901.82*t)+0.1702286306e-1*exp(-0.1544864054e11*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`+.43114634*exp(-0.1544864054e11*t)+24., v[gs](t) = -0.3674479877e-3*exp((30764029.75+1577330139.*I)*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`-0.8037470713e-2*exp((30764029.75+1577330139.*I)*t)-(0.7193539082e-1*I)*exp((30764029.75+1577330139.*I)*t)-(0.3899911367e-2*I)*exp((30764029.75+1577330139.*I)*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`-0.6005358003e-4*exp(-10002901.82*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`-8.504088823*exp(-10002901.82*t)+0.1556340602e-2*exp(-0.1544864054e11*t)*`#msub(mi("V"),mo("in",fontweight = "bold"))`+0.3941819611e-1*exp(-0.1544864054e11*t)+12.}

The <maple> tag doesn't recognize the typesetting codes for V_in: make that

{v[ds](t) = .4958026528*exp((30764029.75+1577330139.*I)*t)*V[`in`]+9.149694069*exp((30764029.75+1577330139.*I)*t)-(.766755745*I)*exp((30764029.75+1577330139.*I)*t)-(0.3290893603e-1*I)*exp((30764029.75+1577330139.*I)*t)*V[`in`]-0.3002643e-3*exp(-10002901.82*t)*V[`in`]-42.51993430*exp(-10002901.82*t)+0.1702286306e-1*exp(-0.1544864054e11*t)*V[`in`]+.43114634*exp(-0.1544864054e11*t)+24., v[gs](t) = -0.3674479877e-3*exp((30764029.75+1577330139.*I)*t)*V[`in`]-0.8037470713e-2*exp((30764029.75+1577330139.*I)*t)-(0.7193539082e-1*I)*exp((30764029.75+1577330139.*I)*t)-(0.3899911367e-2*I)*exp((30764029.75+1577330139.*I)*t)*V[`in`]-0.6005358003e-4*exp(-10002901.82*t)*V[`in`]-8.504088823*exp(-10002901.82*t)+0.1556340602e-2*exp(-0.1544864054e11*t)*V[`in`]+0.3941819611e-1*exp(-0.1544864054e11*t)+12.}

You could also use evalc to express the complex exponentials in terms of real exponentials times sines and cosines.

MaplePrimes - answers and comments on Question, Help! how can i solve this ODE system.

dsolve

tks very much,Robert Israel !

simplification