Internal problem ID [11775]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+8 y=4 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+8*y(x)=4*x^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {23}\, x}{2}\right ) c_{2} +{\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {23}\, x}{2}\right ) c_{1} +\frac {x^{2}}{2}+\frac {3 x}{8}+\frac {1}{64} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 63
DSolve[y''[x]-3*y'[x]+8*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{2}+\frac {3 x}{8}+c_2 e^{3 x/2} \cos \left (\frac {\sqrt {23} x}{2}\right )+c_1 e^{3 x/2} \sin \left (\frac {\sqrt {23} x}{2}\right )+\frac {1}{64} \]