Internal problem ID [1115]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -4 y+6 x +4=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=-6*x-4,x^2],y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{2}}{x^{2}}+x^{2} c_{1}+1+2 x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[x^2*y''[x]+x*y'[x]-4*y[x]==-6*x-4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x^2+\frac {c_1}{x^2}+2 x+1 \\ \end{align*}