Internal problem ID [15406]
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 ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 637.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1}}{x^{2}}+c_{2} \left (x -\frac {3}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 23
DSolve[(x^2-x)*y''[x]+(2*x-3)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^2}+\frac {1}{6} c_2 (3-2 x) \]