59.1.116 problem 118

Internal problem ID [9288]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 118
Date solved : Monday, January 27, 2025 at 06:01:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 23

dsolve(28*x^2*(1-3*x)*diff(y(x),x$2)-7*x*(5+9*x)*diff(y(x),x)+7*(2+9*x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{2}+c_{2} x^{{1}/{4}}}{3 x -1} \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 60

DSolve[28*x^2*(1-3*x)*D[y[x],{x,2}]-7*x*(5+9*x)*D[y[x],x]+7*(2+9*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (4 c_2 x^{7/4}+7 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {6}{3 K[1]-1}-\frac {5}{4 K[1]}\right )dK[1]\right )}{7 x^{3/8}} \]