Internal problem ID [1109]
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: 3.
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 +y-x=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 20
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x,x],y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +\ln \relax (x ) c_{1} x +\frac {\ln \relax (x )^{2} x}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 25
DSolve[x^2*y''[x]-x*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \left (\log ^2(x)+2 c_2 \log (x)+2 c_1\right ) \\ \end{align*}