Internal problem ID [7986]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 510.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 149
dsolve((1+x+2*x^2)*diff(y(x),x$2)+(1+7*x)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (\frac {i \sqrt {7}-4 x -1}{i \sqrt {7}+4 x +1}\right )^{-\frac {3 i \sqrt {7}}{28}} \left (x +1\right )}{\left (2 x^{2}+x +1\right )^{\frac {3}{4}}}+\frac {c_{2} \left (\frac {i \sqrt {7}-4 x -1}{i \sqrt {7}+4 x +1}\right )^{-\frac {3 i \sqrt {7}}{28}} \left (x +1\right ) \left (\int \frac {\left (\frac {i \sqrt {7}+4 x +1}{i \sqrt {7}-4 x -1}\right )^{-\frac {3 i \sqrt {7}}{28}}}{\left (x +1\right )^{2} \left (2 x^{2}+x +1\right )^{\frac {1}{4}}}d x \right )}{\left (2 x^{2}+x +1\right )^{\frac {3}{4}}} \]
✓ Solution by Mathematica
Time used: 2.132 (sec). Leaf size: 102
DSolve[(1+x+2*x^2)*y''[x]+(1+7*x)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(x+1) e^{\frac {3 \arctan \left (\frac {4 x+1}{\sqrt {7}}\right )}{2 \sqrt {7}}} \left (c_2 \int _1^x\frac {e^{-\frac {3 \arctan \left (\frac {4 K[1]+1}{\sqrt {7}}\right )}{2 \sqrt {7}}}}{(K[1]+1)^2 \sqrt [4]{2 K[1]^2+K[1]+1}}dK[1]+c_1\right )}{\left (2 x^2+x+1\right )^{3/4}} \]