40.12.6 problem 11

Internal problem ID [6754]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre). Supplemetary problems. Page 110
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:27:34 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&=6 x \end{align*}

✓ Solution by Maple

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

dsolve((2*x+1)^2*diff(y(x),x$2)-2*(2*x+1)*diff(y(x),x)-12*y(x)=6*x,y(x), singsol=all)
 

\[ y = \frac {c_1}{2 x +1}+\left (2 x +1\right )^{3} c_2 +\frac {-24 x^{2}-8 x -1}{64 x +32} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 41

DSolve[(2*x+1)^2*D[y[x],{x,2}]-2*(2*x+1)*D[y[x],x]-12*y[x]==6*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-24 x^2-8 x+32 c_1 (2 x+1)^4-1+32 c_2}{32 (2 x+1)} \]