12.9.5 problem 5

Internal problem ID [1761]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:34:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=7 x^{{3}/{2}} {\mathrm e}^{x} \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\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)=7*x^(3/2)*exp(x),exp(x)],singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_2 +c_1 x +\frac {4 x^{{7}/{2}}}{5}\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==7*x^(3/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^x \left (4 x^{7/2}+5 c_2 x+5 c_1\right ) \]