What is the solution for (x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0 ?

The solution for (x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0 is y=e^{x+c_{1}}x-e^{x+c_{1}}+c_{2}x

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(x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0

(x^{2} - x + 1) y^{^{''}} - (x^{2} + x) y^{^{'}} + (x + 1) y = 0

y = e^{x + c_{1}} x - e^{x + c_{1}} + c_{2} x

Solution steps

(x^{2} - x + 1) y^{''} (x) - (x^{2} + x) y^{'} (x) + (x + 1) y = 0

Solve using substitution:

y = e^{x + c_{1}} x - e^{x + c_{1}} + c_{2} x

y = e^{x + c_{1}} x - e^{x + c_{1}} + c_{2} x

What is the solution for (x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0 ?
The solution for (x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0 is y=e^{x+c_{1}}x-e^{x+c_{1}}+c_{2}x