Internal problem ID [11820]
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: 46.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }=x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x} x +5 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+2*diff(y(x),x)=x^2*exp(x)+3*x*exp(2*x)+5*x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (6 x^{2}+4 c_{1} -18 x +21\right ) {\mathrm e}^{2 x}}{8}+\frac {\left (-x^{3}+3 c_{2} -6 x +6\right ) {\mathrm e}^{x}}{3}+\frac {5 x^{3}}{6}+\frac {15 x^{2}}{4}+\frac {35 x}{4}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.885 (sec). Leaf size: 67
DSolve[y'''[x]-3*y''[x]+2*y'[x]==x^2*Exp[x]+3*x*Exp[2*x]+5*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {5 x^3}{6}+e^x \left (-\frac {x^3}{3}-2 x+c_1\right )+\frac {15 x^2}{4}+\frac {1}{8} e^{2 x} \left (6 x^2-18 x+21+4 c_2\right )+\frac {35 x}{4}+c_3 \]