Internal problem ID [1183]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y-x^{\frac {5}{2}} {\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.035 (sec). Leaf size: 24
dsolve(4*x^2*diff(y(x),x$2)-4*x*(x+1)*diff(y(x),x)+(2*x+3)*y(x)=x^(5/2)*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, c_{2}+\sqrt {x}\, {\mathrm e}^{x} c_{1}+\frac {x^{\frac {3}{2}} {\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 30
DSolve[4*x^2*y''[x]-4*x*(x+1)*y'[x]+(2*x+3)*y[x]==x^(5/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \sqrt {x} \left (e^x (x-1+4 c_2)+4 c_1\right ) \\ \end{align*}