Internal problem ID [1184]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y-\left (3 x -1\right )^{2} {\mathrm e}^{2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 28
dsolve([(3*x-1)*diff(y(x),x$2)-(3*x+2)*diff(y(x),x)-(6*x-8)*y(x)=(3*x-1)^2*exp(2*x),y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (3 x^{2}-2 x +6\right ) {\mathrm e}^{2 x}}{6}+\frac {x \,{\mathrm e}^{-x}}{3} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 33
DSolve[{(3*x-1)*y''[x]-(3*x+2)*y'[x]-(6*x-8)*y[x]==(3*x-1)^2*Exp[2*x],{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-x} \left (2 x+e^{3 x} (x (3 x-2)+6)\right ) \\ \end{align*}