Internal problem ID [2523]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y=x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve((x+1)^2*diff(y(x),x$2)+3*(x+1)*diff(y(x),x)+y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (18 c_{1} -6\right ) \ln \left (x +1\right )+2 x^{3}-3 x^{2}+6 x +18 c_{2}}{18 x +18} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 44
DSolve[(x+1)^2*y''[x]+3*(x+1)*y'[x]+y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 x^3-3 x^2+6 x+6 (-1+3 c_2) \log (x+1)+18 c_1}{18 (x+1)} \]