Internal problem ID [8864]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1284.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 42
dsolve((2*x+1)^2*diff(diff(y(x),x),x)-2*(2*x+1)*diff(y(x),x)-12*y(x)-3*x-1=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{2 x +1}+\left (2 x +1\right )^{3} c_{2}-\frac {72 x^{2}+56 x +7}{192 \left (2 x +1\right )} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 41
DSolve[-1 - 3*x - 12*y[x] - 2*(1 + 2*x)*y'[x] + (1 + 2*x)^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-72 x^2-56 x+192 c_1 (2 x+1)^4-7+192 c_2}{192 (2 x+1)} \\ \end{align*}