Internal problem ID [7644]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 156.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x \left (x^{2}+1\right ) y^{\prime \prime }+\left (1-x^{2}\right ) y^{\prime }-8 y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 71
dsolve(x*(1+x^2)*diff(y(x),x$2)+(1-x^2)*diff(y(x),x)-8*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{4}+2 x^{2}+1\right )+c_{2} \left (-\frac {\ln \left (x^{2}+1\right ) x^{4}}{2}+x^{4} \ln \left (x \right )-\ln \left (x^{2}+1\right ) x^{2}+2 x^{2} \ln \left (x \right )+\frac {x^{2}}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+\ln \left (x \right )+\frac {3}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 55
DSolve[x*(1+x^2)*y''[x]+(1-x^2)*y'[x]-8*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \left (x^2+1\right )^2+\frac {1}{4} c_2 \left (2 x^2+4 \left (x^2+1\right )^2 \log (x)-2 \left (x^2+1\right )^2 \log \left (x^2+1\right )+3\right ) \]