Internal problem ID [2312]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.9, Reduction of Order. page
572
Problem number: Problem 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y-15 \,{\mathrm e}^{3 x} \sqrt {x}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{3 x} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=15*exp(3*x)*sqrt(x),exp(3*x)],y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+x \,{\mathrm e}^{3 x} c_{1}+4 x^{\frac {5}{2}} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 25
DSolve[y''[x]-6*y'[x]+9*y[x]==15*Exp[3*x]*Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x} \left (4 x^{5/2}+c_2 x+c_1\right ) \\ \end{align*}