Internal problem ID [11299]
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: 0.0 (sec). Leaf size: 53
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x +\left (6 \left (-x^{3}\right )^{\frac {1}{3}} 3^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )-6 \left (-x^{3}\right )^{\frac {1}{3}} 3^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )+18 \,{\mathrm e}^{\frac {x^{3}}{3}}\right ) c_{1} +1 \]
✓ 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]
\[ y(x)\to -\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (-\frac {1}{3},-\frac {x^3}{3}\right )}{3 \sqrt [3]{3}}+c_1 x+1 \]