Internal problem ID [12263]
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]]
\[ \boxed {y^{\prime \prime }+x^{2} y^{\prime }+2 y x=2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 66
dsolve(diff(y(x),x$2)+x^2*diff(y(x),x)+2*x*y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 x \Gamma \left (\frac {1}{3}, -\frac {x^{3}}{3}\right ) c_{1} \Gamma \left (\frac {2}{3}\right ) {\mathrm e}^{-\frac {x^{3}}{3}}+\left (\left (c_{2} -1\right ) \left (-x^{3}\right )^{\frac {1}{3}}-2 x \sqrt {3}\, \pi c_{1} \right ) {\mathrm e}^{-\frac {x^{3}}{3}}+\left (-x^{3}\right )^{\frac {1}{3}}}{\left (-x^{3}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 59
DSolve[y''[x]+x^2*y'[x]+2*x*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^{-\frac {x^3}{3}}+\frac {c_1 e^{-\frac {x^3}{3}} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {x^3}{3}\right )}{3^{2/3} x^2}+1 \]