9.5 problem 5

Internal problem ID [1111]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-7 x^{\frac {3}{2}} {\mathrm e}^{x}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \end {align*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=7*x^(3/2)*exp(x),exp(x)],y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{1}+\frac {4 x^{\frac {7}{2}} {\mathrm e}^{x}}{5} \]

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {1}{5} e^x \left (4 x^{7/2}+5 c_2 x+5 c_1\right ) \\ \end{align*}