What is the solution for x^3y^{'''}+xy^'-y=x^2 ?

The solution for x^3y^{'''}+xy^'-y=x^2 is y=c_{1}x+c_{2}ln(x)x+c_{3}ln^2(x)x+x^2

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x^3y^{'''}+xy^'-y=x^2

x^{3} y^{^{'''}} + x y^{^{'}} - y = x^{2}

y = c_{1} x + c_{2} ln (x) x + c_{3} ln^{2} (x) x + x^{2}

Solution steps

x^{3} y^{'''} (x) + x y^{'} (x) - y = x^{2}

Solve linear ODE:

y = c_{1} x + c_{2} ln (x) x + c_{3} ln^{2} (x) x + x^{2}

y = c_{1} x + c_{2} ln (x) x + c_{3} ln^{2} (x) x + x^{2}

What is the solution for x^3y^{'''}+xy^'-y=x^2 ?
The solution for x^3y^{'''}+xy^'-y=x^2 is y=c_{1}x+c_{2}ln(x)x+c_{3}ln^2(x)x+x^2