59.1.684 problem 701

Internal problem ID [9856]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 701
Date solved : Monday, January 27, 2025 at 06:15:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 21

dsolve((4*x^3-14*x^2-2*x)*diff(y(x),x$2)-(6*x^2-7*x+1)*diff(y(x),x)+(6*x-1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.956 (sec). Leaf size: 155

DSolve[(4*x^3-14*x^2-2*x)*D[y[x],{x,2}]-(6*x^2-7*x+1)*D[y[x],x]+(6*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x-1) \exp \left (\int _1^x\frac {6 K[1]^2-7 K[1]+1}{-8 K[1]^3+28 K[1]^2+4 K[1]}dK[1]-\frac {1}{2} \int _1^x\left (\frac {7-4 K[2]}{K[2] (2 K[2]-7)-1}+\frac {1}{2 K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[3]}\frac {6 K[1]^2-7 K[1]+1}{-8 K[1]^3+28 K[1]^2+4 K[1]}dK[1]\right )}{(K[3]-1)^2}dK[3]+c_1\right ) \]