Internal problem ID [5406]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre).
Supplemetary problems. Page 110
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y=x +\ln \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x+x^2*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (x \right )^{3} x^{2}}{6}+\ln \left (x \right ) x^{2} c_{1} +c_{2} x^{2}+x \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 30
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==x+x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} x \left (x \log ^3(x)+6 c_1 x+12 c_2 x \log (x)+6\right ) \]