Internal problem ID [11852]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y=\left (2 x +1\right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve((2*x+1)*(x+1)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=(2*x+1)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 x^{3}+\left (6 c_{1} +24 c_{2} +4\right ) x^{2}+\left (6 c_{1} +24 c_{2} +1\right ) x +6 c_{2}}{6 x +6} \]
✓ Solution by Mathematica
Time used: 1.049 (sec). Leaf size: 72
DSolve[(2*x+1)*(x+1)*y''[x]+2*x*y'[x]-2*y[x]==(2*x+1)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {-2 x-1} (4 x+3) x^2-6 c_2 (x+1) \sqrt {2 x+1} x+6 c_1 \sqrt {2 x+1}}{6 \sqrt {-2 x-1} (x+1)} \]