77.1.112 problem 140 (page 204)

Internal problem ID [18002]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 140 (page 204)
Date solved : Tuesday, January 28, 2025 at 11:19:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=x -1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

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

\[ y = c_{2} x +{\mathrm e}^{x} c_{1} -x^{2}-1 \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 25

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

\[ y(x)\to -x^2-(1+c_2) x+c_1 e^x-1 \]