60.3.279 problem 1284

Internal problem ID [11289]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1284
Date solved : Monday, January 27, 2025 at 11:05:15 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 41

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)
 

\[ y = \frac {c_{1}}{2 x +1}+\left (2 x +1\right )^{3} c_{2} +\frac {-72 x^{2}-56 x -7}{384 x +192} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 41

DSolve[-1 - 3*x - 12*y[x] - 2*(1 + 2*x)*D[y[x],x] + (1 + 2*x)^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-72 x^2-56 x+192 c_1 (2 x+1)^4-7+192 c_2}{192 (2 x+1)} \]