Internal problem ID [11048]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto.
Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS.
Problems page 28
Problem number: Problem 1.3(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y-x^{\frac {3}{2}} {\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x^(3/2)*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 x^{\frac {7}{2}} {\mathrm e}^{x}}{35}+c_{1} x \,{\mathrm e}^{x}+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[y''[x]-2*y'[x]+y[x]==x^(3/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{35} e^x \left (4 x^{7/2}+35 c_2 x+35 c_1\right ) \\ \end{align*}