Internal problem ID [11729]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
124
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=4 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=4*x^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{x}+2 x^{2}+6 x +7 \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 29
DSolve[y''[x]-3*y'[x]+2*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^2+6 x+c_1 e^x+c_2 e^{2 x}+7 \]