75.20.2 problem 637

Internal problem ID [17136]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 637
Date solved : Tuesday, January 28, 2025 at 09:54:02 AM
CAS classification : [_Jacobi]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 107

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

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