Internal problem ID [11289]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 53. Change of
dependent variable. Page 125
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-x^{2} y^{\prime }+y x=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 57
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-3^{\frac {1}{3}} {\mathrm e}^{\frac {x^{3}}{3}} c_{1} -c_{2} x -1\right ) \left (-x^{3}\right )^{\frac {2}{3}}+x^{3} c_{1} \left (\Gamma \left (\frac {2}{3}\right )-\Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )\right )}{\left (-x^{3}\right )^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 0.286 (sec). Leaf size: 42
DSolve[y''[x]-x^2*y'[x]+x*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (-\frac {1}{3},-\frac {x^3}{3}\right )}{3 \sqrt [3]{3}}+c_1 x+1 \]