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}

\int 20 x^{3} (5 x^{4} + 6)^{3} d x

x \to 4 - lim (\frac{x}{x - 2})

\frac{1}{x}, 1, 33

\int \frac{42 x ^{2}}{x ^{4} - 29 x ^{2} + 100} d x

x^{2} + 8 y^{2} = 8

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