Internal problem ID [12260]
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]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y=-2 x +1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve((1-x^2)*diff(y(x),x$2)+(1-x)*diff(y(x),x)+y(x)=1-2*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (c_{1} +2\right ) \left (-1+x \right ) \ln \left (-1+x \right )}{4}-\frac {\left (-2+c_{1} \right ) \left (-1+x \right ) \ln \left (1+x \right )}{4}+c_{2} x +\frac {c_{1}}{2}-c_{2} \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 74
DSolve[(1-x^2)*y''[x]+(1-x)*y'[x]+y[x]==1-2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} ((x-1) \log (1-x)+2 x \log (x+1)-2 \log (x+1)-4 c_1 x+(1+c_2) (x-1) \log (x-1)-c_2 x \log (x+1)+c_2 \log (x+1)+4 c_1+2 c_2) \]