58.2.21 problem 22
Internal
problem
ID
[9144]
Book
:
Second
order
enumerated
odes
Section
:
section
2
Problem
number
:
22
Date
solved
:
Tuesday, January 28, 2025 at 04:00:10 PM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y&=4 \cos \left (\ln \left (1+x \right )\right ) \end{align*}
✓ Solution by Maple
Time used: 0.077 (sec). Leaf size: 280
dsolve((1+x^2)*diff(y(x),x$2)+(1+x)*diff(y(x),x)+y(x)=4*cos(ln(1+x)),y(x), singsol=all)
\[
y = \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right ) c_{2} +\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 ) c_{1} -80 \left (\int \frac {\left (i x -1\right ) \cos \left (\ln \left (x +1\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}-\frac {i x}{2}\right )}{\left (x^{2}+1\right ) \left (10 \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 ) \left (\left (-1-i+\left (-1+i\right ) x \right ) \operatorname {hypergeom}\left (\left [1-i, 1+i\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )+\left (1+i\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )\right )+\operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\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}-\frac {i x}{2}\right ) \left (1+7 i+\left (7-i\right ) x \right )\right )}d x \right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )-80 \left (\int \frac {\operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right ) \cos \left (\ln \left (x +1\right )\right ) \left (x +i\right )^{\frac {1}{2}+\frac {i}{2}}}{7 \left (\frac {10 \left (\left (1-i+\left (-1-i\right ) x \right ) \operatorname {hypergeom}\left (\left [1-i, 1+i\right ], \left [\frac {3}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )+\left (-1+i\right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{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}-\frac {i x}{2}\right )}{7}+\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}-\frac {i x}{2}\right ) \left (-1+\frac {i}{7}+\left (\frac {1}{7}+i\right ) x \right ) \operatorname {hypergeom}\left (\left [i, -i\right ], \left [\frac {1}{2}+\frac {i}{2}\right ], \frac {1}{2}-\frac {i x}{2}\right )\right ) \left (x^{2}+1\right )}d x \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 )
\]
✗ Solution by Mathematica
Time used: 0.000 (sec). Leaf size: 0
DSolve[(1+x^2)*D[y[x],{x,2}]+(1+x)*D[y[x],x]+y[x]==4*Cos[Log[1+x]],y[x],x,IncludeSingularSolutions -> True]
Not solved