82.38.2 problem Ex. 2

Internal problem ID [18932]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. Problems at page 91
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:37:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve((2*x-1)^3*diff(y(x),x$2)+(2*x-1)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left ({\mathrm e}^{\frac {1}{4 x -2}} c_{1} +c_{2} \right ) \left (2 x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 27

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

\[ y(x)\to -\left ((2 x-1) \left (c_1 e^{\frac {1}{4 x-2}}+c_2\right )\right ) \]