Internal problem ID [11939]
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(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x=2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(diff(y(x),x$2)+2*x^2*diff(y(x),x)+4*x*y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\frac {2 x^{3}}{3}} x \left (2 \sqrt {3}\, \pi -3 \Gamma \left (\frac {1}{3}, -\frac {2 x^{3}}{3}\right ) \Gamma \left (\frac {2}{3}\right )\right ) c_{1}}{\left (-x^{3}\right )^{\frac {1}{3}}}+{\mathrm e}^{-\frac {2 x^{3}}{3}} c_{2} +\frac {\left (-1+{\mathrm e}^{\frac {2 x^{3}}{3}}\right ) {\mathrm e}^{-\frac {2 x^{3}}{3}}}{2} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 66
DSolve[y''[x]+2*x^2*y'[x]+4*x*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 e^{-\frac {2 x^3}{3}}+\frac {c_1 e^{-\frac {2 x^3}{3}} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {2 x^3}{3}\right )}{\sqrt [3]{2} 3^{2/3} x^2}+\frac {1}{2} \]