Internal problem ID [5417]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y=\left (-x^{2}+6\right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-x*(2*x+3)*diff(y(x),x)+(x^2+3*x+3)*y(x)=(6-x^2)*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{1} x^{3}+c_{2} x +x^{2}+2\right ) \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 30
DSolve[x^2*y''[x]-x*(2*x+3)*y'[x]+(x^2+3*x+3)*y[x]==(6-x^2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x \left (c_2 x^3+2 x^2+2 c_1 x+4\right ) \]