This is very odd as it is a really simple ODE and the interpretation of the input seems correct, yet Wolfram Alpha produces rubbish: $$x'' - 2x' + x = t, \quad x(0) = 1.$$ Wolfram Alpha claims that the solution to this is $x(t) = c_1e^tt$ (Link). For reference, it gets it correct if you either put none or two initial conditions (Link,Link). Is this a known issue?
2026-03-26 17:30:40.1774546240
Why does Wolfram Alpha give a wrong answer to a linear ODE with constant coefficients?
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There is nothing wrong with step-by-step. It gives correct solution. This could be just a final display bug where it did not format the answer correctly on the screen.
Here is the step-by-step solution from Wolfram alpha. If you have Mathematica, no need for PRO account. As one can issue the Wolfram alpha command from inside Mathematica and get the step-by-step solution that way. Now, clicking on the button there which says "step-by-step" gives
So you see, it does solve it correctly. But the final output where it says "Differential equation solutions" is not the same as the final answer in the step-by-step. So looks like a software bug in final display of solution.
I think this question is better posted at Wolfram community where Wolfram developers can more easily see it and fix the bug.