Internal problem ID [6451]
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]]
\[ \boxed {x^{4} y^{\prime \prime }+y^{\prime } x^{3}-4 y x^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {c_{2}}{x^{2}}+x^{2} c_{1} +\frac {-4 \ln \left (x \right )-1}{16 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (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*}