83.47.9 problem Ex 9 page 89

Internal problem ID [19586]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 9 page 89
Date solved : Tuesday, January 28, 2025 at 08:32:55 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

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

\[ y \left (x \right ) = c_{1} x -\frac {c_{1}}{2}+c_{2} \left (x -\frac {1}{2}\right )^{\frac {\sqrt {3}}{2}+1}+c_3 \left (x -\frac {1}{2}\right )^{1-\frac {\sqrt {3}}{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 50

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

\[ y(x)\to (2 x-1) \left (c_2 (2 x-1)^{\frac {\sqrt {3}}{2}}+c_1 (2 x-1)^{-\frac {\sqrt {3}}{2}}+c_3\right ) \]