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Reported: [CASE:5287941] DSolve gives wrong solution. V 14.3

Using V 14.3, why DSolve gives solution $y=0$ which satisfies the IC given, but not the ode itself?

ode=Cos[x]*D[y[x],{x,2}]+3*y[x]==1; (* ID #22122*) ic={y[1]==0,Derivative[1][y][0]==0}; sol=DSolve[{ode,ic},y,x]

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ode /. sol

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ic /. sol

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Does this happen also in earlier versions? I tried it on V 14.2 and it gives same result.

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    $\begingroup$ Version 13.0.1 returns {}. $\endgroup$ Commented Aug 28 at 21:47
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    $\begingroup$ V12.0 returns the input with and without the ic specified. V14.3 returns interesting result without the ic and will not verify satisfying the ode. $\endgroup$ Commented Aug 28 at 21:55
  • $\begingroup$ Maybe because of this: {y[0] == 0 /. First@DSolve[ode, y, x], y'[0] == 0 /. First@DSolve[ode, y, x]} // Solve[#, {C[1], C[2]}] & $\endgroup$ Commented Aug 28 at 23:05
  • $\begingroup$ @MichaelE2 I think you mean y[1]==0 in there and not y[0] == 0. But we get same result anyway, which is that $c_1=0,c_2=0$ which gives $y=0$ solution. But I would think that DSolve should check again now that the solution satisfies the ode also, and not just the IC. It seems then DSolve does not do this extra check, which is strange. $\endgroup$ Commented Aug 29 at 1:47
  • $\begingroup$ Oops, yes, y[1]==0. I don't have time to spelunk it, but it certainly seems a bug. $\endgroup$ Commented Aug 29 at 2:14

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