59.1.149 problem 151

Internal problem ID [9321]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 151
Date solved : Monday, January 27, 2025 at 06:01:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

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

\[ y = \frac {3 c_{2} \ln \left (x \right )+\left (-8 x^{3}+18 x^{2}-18 x \right ) c_{2} +c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 105

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

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