Internal problem ID [1123]
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: 17.
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 }-5 y^{\prime } x +8 y-4 x^{2}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+8*y(x)=4*x^2,x^2],y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+x^{4} c_{1}-2 \ln \relax (x ) x^{2}-x^{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[x^2*y''[x]-5*x*y'[x]+8*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (c_2 x^2-2 \log (x)-1+c_1\right ) \\ \end{align*}