Internal problem ID [6452]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }+y^{\prime } x^{3}-4 x^{2} y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x^4*diff(y(x),x$2)+x^3*diff(y(x),x)-4*x^2*y(x)=1,y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\frac {c_{1}}{x^{2}}+\frac {-1-4 \ln \relax (x )}{16 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 29
DSolve[x^4*y''[x]+x^3*y'[x]-4*x^2*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {16 c_2 x^4-4 \log (x)-1+16 c_1}{16 x^2} \\ \end{align*}