68.1.3 problem Problem 1.3(a)

Internal problem ID [14132]
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)
Date solved : Tuesday, January 28, 2025 at 06:15:27 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=x^{{3}/{2}} {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x^(3/2)*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_{2} +c_{1} x +\frac {4 x^{{7}/{2}}}{35}\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==x^(3/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{35} e^x \left (4 x^{7/2}+35 c_2 x+35 c_1\right ) \]