Internal problem ID [10915]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 18(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+x^{2} y^{\prime }+2 x y-2 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x$2)+x^2*diff(y(x),x)+2*x*y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (2 \sqrt {3}\, \pi -3 \Gamma \left (\frac {1}{3}, -\frac {x^{3}}{3}\right ) \Gamma \left (\frac {2}{3}\right )\right ) {\mathrm e}^{-\frac {x^{3}}{3}} c_{1}}{\left (-x^{3}\right )^{\frac {1}{3}}}+{\mathrm e}^{-\frac {x^{3}}{3}} c_{2} +\left (-1+{\mathrm e}^{\frac {x^{3}}{3}}\right ) {\mathrm e}^{-\frac {x^{3}}{3}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 41
DSolve[y''[x]+x^2*y'[x]+2*x*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {1}{3} e^{-\frac {x^3}{3}} \left (3 c_2-c_1 x \operatorname {ExpIntegralE}\left (\frac {2}{3},-\frac {x^3}{3}\right )\right ) \\ \end{align*}