67.2.58 problem Problem 20(e)

Internal problem ID [14015]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(e)
Date solved : Tuesday, January 28, 2025 at 06:12:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 43

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

\[ y = \frac {\left (2 \ln \left (x \right ) x^{2}+4 x -1\right ) c_{2} +c_{1} x^{2}+\frac {x^{3} \left (x^{2}-3 x +3\right )}{3}}{\left (x -1\right )^{3}} \]

✓ Solution by Mathematica

Time used: 0.384 (sec). Leaf size: 285

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

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