Internal problem ID [10912]
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 18(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y+2 x -1=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve((1-x^2)*diff(y(x),x$2)+(1-x)*diff(y(x),x)+y(x)=1-2*x,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {\ln \left (x +1\right ) x}{4}+\frac {\ln \left (x +1\right )}{4}+\frac {1}{2}+\frac {\ln \left (x -1\right ) x}{4}-\frac {\ln \left (x -1\right )}{4}\right ) c_{1} +\left (x -1\right ) c_{2} +\frac {\left (\ln \left (x +1\right )+\ln \left (x -1\right )\right ) \left (x -1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 56
DSolve[(1-x^2)*y''[x]+(1-x)*y'[x]+y[x]==1-2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} ((x-1) \log (1-x)-4 c_1 (x-1)+(1+c_2) (x-1) \log (x-1)-(-2+c_2) (x-1) \log (x+1)+2 c_2) \\ \end{align*}