Internal problem ID [5418]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }+4 y^{\prime } x^{3}+\left (x^{2}+1\right )^{2} y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(4*x^2*diff(y(x),x$2)+4*x^3*diff(y(x),x)+(x^2+1)^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x}\, {\mathrm e}^{-\frac {x^{2}}{4}} \left (c_{2} \ln \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 28
DSolve[4*x^2*y''[x]+4*x^3*y'[x]+(x^2+1)^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {x^2}{4}} \sqrt {x} (c_2 \log (x)+c_1) \]