Asking Wolfram|Alpha to find particular solution with boundary conditions?

Questions
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1

For example I am asked to ‘Find the particular solution of the differential equation having the given boundary conditions’.

dy/dx = 3x^2-2x+1
when x = 4, y = 1

I understand how to do this problem, I find the integral:

y = x^3-x^2+x-C

Then I set y to 1 and x to 4 and solve for C which comes out to -51.

So the answer turns out to be x^3-x^2+x-51
Is there anyway to ask WA to do the entire problem? I know I can break it up by first asking for the indefinite integral and then asking it to solve the equation separately.

2

I tried NDSolve[{y'[x] - 3 x^2 + 2 x - 1 == 0, y[4] == 1}, y[x], x] and also tried the same using DSolve in WolframAlpha. I don’t think either are supported, so I just threw it in Mathematica and obtained the following (see attachment)

3

With Wolfram Alpha, just type in y’[x]=3x^2-2x+1, y[4]=1

The knowledge engine will infer that you might want the solution.

Here is a link y’[x]=3x^2-2x+1, y[4]=1