67.2.29 problem Problem 5(c)
Internal
problem
ID
[13986]
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)
Date
solved
:
Tuesday, January 28, 2025 at 08:25:07 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \end{align*}
With initial conditions
\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}
✓ Solution by Maple
Time used: 0.685 (sec). Leaf size: 100
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)
\[
y = \frac {-20 \,{\mathrm e}^{\left (\frac {1}{4}-\frac {i}{4}\right ) \pi } \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right ) \left (x +i\right )^{\frac {1}{2}+\frac {i}{2}} \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )+20 \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )}{\left (10-10 i\right ) \left (\operatorname {hypergeom}\left (\left [1-i, 1+i\right ], \left [\frac {3}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )-\operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {i}{2}, \frac {1}{2}+\frac {3 i}{2}\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}\right )+\left (-1+7 i\right ) \operatorname {hypergeom}\left (\left [\frac {3}{2}+\frac {3 i}{2}, \frac {3}{2}-\frac {i}{2}\right ], \left [\frac {5}{2}+\frac {i}{2}\right ], \frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}-\frac {i}{2}\right ], \frac {1}{2}\right )}
\]
✗ Solution by Mathematica
Time used: 0.000 (sec). Leaf size: 0
DSolve[{(x^2+1)*D[y[x],{x,2}]+(x-1)*D[y[x],x]+y[x]==0,{y[0]==0,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
Not solved