Internal problem ID [11810]
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: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=3 x^{2} {\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve([diff(y(x),x$2)-y(x)=3*x^2*exp(x),y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x}}{8}+\frac {\left (4 x^{3}-6 x^{2}+6 x +9\right ) {\mathrm e}^{x}}{8} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 37
DSolve[{y''[x]-y[x]==3*x^2*Exp[x],{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} e^{-x} \left (e^{2 x} \left (4 x^3-6 x^2+6 x+9\right )-1\right ) \]