Internal problem ID [699]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y=\ln \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x) = x^2*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = x^{2} c_{2} +\ln \left (x \right ) c_{1} x^{2}+\frac {\ln \left (x \right )^{3} x^{2}}{6} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 27
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x] == x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} x^2 \left (\log ^3(x)+12 c_2 \log (x)+6 c_1\right ) \]