Internal problem ID [12250]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 5(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } \left (x -1\right )+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 157
dsolve([(x^2+1)*diff(y(x),x$2)+(x-1)*diff(y(x),x)+y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-20 \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right ) {\mathrm e}^{\left (\frac {1}{4}-\frac {i}{4}\right ) \pi } \left (x +i\right )^{\frac {1}{2}+\frac {i}{2}} \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )+20 \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )}{\left (10-10 i\right ) \left (\operatorname {hypergeom}\left (\left [1-i, 1+i\right ], \left [\frac {3}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )-\operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}\right )+\left (-1+7 i\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}+\frac {3 i}{2}, \frac {3}{2}-\frac {i}{2}\right ], \left [\frac {5}{2}+\frac {i}{2}\right ], \frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(x^2+1)*y''[x]+(x-1)*y'[x]+y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
Not solved