# Making boundary condition a variable in ParametricNDSolve

I would like to make where my ODE is evaluated at (not the boundary condition itself but rather the "x" value of the boundary condition) to be a variable in my code. I find that Mathematica complains that it cannot find a starting value for ParametricNDSolve. My code is as follows:

    a321 = {-7, -(19/6), 41/10};

b321 =  {
{-26, 9/2, 11/10},
{12, 35/6, 9/10},
{44/5, 27/10, 199/50}
} ;

ainv3221[u_] = {1/v4[u], 1/v3[u], 1/v2[u], 1/v1[u]};

sol = ParametricNDSolve[{
v4'[u] -
1/u Part[-(a3221/(2 \[Pi])) -
1/(8 \[Pi]^2) b3221 .ainv3221[u], 1] == 0,
v3'[u] -
1/u Part[-(a3221/(2 \[Pi])) -
1/(8 \[Pi]^2) b3221 .ainv3221[u], 2] == 0,
v2'[u] -
1/u Part[-(a3221/(2 \[Pi])) -
1/(8 \[Pi]^2) b3221 . ainv3221[u], 3] == 0,
v1'[u] -
1/u Part[-(a3221/(2 \[Pi])) -
1/(8 \[Pi]^2) b3221 . ainv3221[u], 4] == 0,
v4[t] == b1,
v3[t] == b2,
v2[t] == b3,
v1[t] == b4},
{v1, v2, v3, v4}, {u, 10^1, 10^17}, {t, b1, b2, b3,
b4}];
v1sol[t_, b1_, b2_, b3_, b4_] := v1[t, b1, b2, b3, b4][u] /. sol;
v2sol[t_, b1_, b2_, b3_, b4_] := v2[t, b1, b2, b3, b4][u] /. sol;
v3sol[t_, b1_, b2_, b3_, b4_] := v3[t, b1, b2, b3, b4][u] /. sol;
v4sol[t_, b1_, b2_, b3_, b4_] := v4[t, b1, b2, b3, b4][u] /. sol;


I would like to get v1sol, v2sol, v3sol and v4sol such that I can vary where the boundary condition are satisfied. Varying the boundary condition itself (say b1 = 34, b2 = 45, b3 = 55, b4 = 65) is not a problem but varying "t" is.

Any help is appreciated.

• Try sol[t_, b1_, b2_, b3_, b4_] := NDSolve[.... Mar 31 at 1:08
• I did but that also don't allow you to make the boundary condition (or where the boundary is evaluated) a variable Mar 31 at 6:23
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• By the way, a3221 and b3221 are undefined, and a321 and b321have a different dimension than ainv3221. Apr 1 at 1:09

s[x0_] := NDSolveValue[{y'[x] == 1, y[x0] == 0}, y[x], {x, 0, 5}]

s[x0_, y0_] := NDSolveValue[{y'[x] == 1, y[x0] == y0}, y[x], {x, 0, 5}]