With an view to see how (a multiplicative) mixture would play out, checked some ODE options:

xm = 8;
NDSolve[{(y'[x] - 0.5) == 0, y[1] == 1}, y, {x, 1, xm}];
yy[x_] = y[x] /. First[%];
g1 = Plot[yy[x], {x, 1, xm}, GridLines -> Computerized]
NDSolve[{(y''[x] + y[x]) == 0, y[1] == 1, y'[1] == 1.5}, 
  y, {x, 1, xm}];
yy[x_] = y[x] /. First[%];
g2 = Plot[yy[x], {x, 1, xm}, GridLines -> Computerized]
Present[{g1, g2}, PlotRange -> All]
NDSolve[{(y''[x] + y[x])*(y'[x] - 0.5) == 0, y[1] == 1, y'[1] == 1.5},
   y, {x, 1, xm}];
yy[x_] = y[x] /. First[%];
g3 = Plot[yy[x], {x, 1, xm}, 
  PlotLabel -> "StraightLine_Ignored_in_Combo", GridLines -> Computerized]
NDSolve[{(y''[x] + y[x])*(y''[x] + x/12) == 0, y[1] == 1, y'[1] == 0},
   y, {x, 1, xm}];
yy[x_] = y[x] /. First[%];
g4 = Plot[yy[x], {x, 1, xm}, GridLines -> Computerized, 
  PlotLabel -> " SINE_CURVE_IGNORED_IN_COMBO"]

No new built-in / artificial curve is seen however solely a choose output of one of many two. Am not now capable of finding a foundation of this selection. I hope you’d assist right here, additionally with normal feedback about success with such combos.