Internal problem ID [6709]
Book: Second order enumerated odes
Section: section 2
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }+4 y x^{3}-x^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 22
dsolve(x*diff(y(x),x$2)-diff(y(x),x)+4*x^3*y(x)=x^5,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (x^{2}\right ) c_{2}+\cos \left (x^{2}\right ) c_{1}+\frac {x^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 27
DSolve[x*y''[x]-y'[x]+4*x^3*y[x]==x^5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{4}+c_1 \cos \left (x^2\right )+c_2 \sin \left (x^2\right ) \\ \end{align*}