Internal problem ID [1189]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y-\left (2 x +3\right )^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([(x+1)*(2*x+3)*diff(y(x),x$2)+2*(x+2)*diff(y(x),x)-2*y(x)=(2*x+3)^2,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (4 x +9\right )}{6 x +6} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 22
DSolve[{(x+1)*(2*x+3)*y''[x]+2*(x+2)*y'[x]-2*y[x]==(2*x+3)^2,{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 (4 x+9)}{6 (x+1)} \\ \end{align*}