56.3.19 problem 19
Internal
problem
ID
[8877]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
3.0
Problem
number
:
19
Date
solved
:
Monday, January 27, 2025 at 05:11:32 PM
CAS
classification
:
[[_3rd_order, _with_linear_symmetries]]
\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=x \end{align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 223
dsolve(x^4*diff(y(x),x$3)+x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+x*y(x)= x,y(x), singsol=all)
\[
y = c_{2} x^{\frac {\left (47-3 \sqrt {249}\right ) \left (188+12 \sqrt {249}\right )^{{2}/{3}}}{192}+\frac {\left (188+12 \sqrt {249}\right )^{{1}/{3}}}{12}+\frac {2}{3}} \cos \left (\frac {\left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}} \sqrt {3}\, \left (3 \sqrt {3}\, \sqrt {83}\, \left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}}-47 \left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}}+16\right ) \ln \left (x \right )}{192}\right )+c_3 \,x^{\frac {\left (47-3 \sqrt {249}\right ) \left (188+12 \sqrt {249}\right )^{{2}/{3}}}{192}+\frac {\left (188+12 \sqrt {249}\right )^{{1}/{3}}}{12}+\frac {2}{3}} \sin \left (\frac {\left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}} \sqrt {3}\, \left (3 \sqrt {3}\, \sqrt {83}\, \left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}}-47 \left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}}+16\right ) \ln \left (x \right )}{192}\right )+x^{\frac {\left (-47+3 \sqrt {249}\right ) \left (188+12 \sqrt {249}\right )^{{2}/{3}}}{96}-\frac {\left (188+12 \sqrt {249}\right )^{{1}/{3}}}{6}+\frac {2}{3}} c_{1} +1
\]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 82
DSolve[x^4*D[y[x],{x,3}]+x^3*D[y[x],{x,2}]+x^2*D[y[x],x]+x*y[x]== x,y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to c_1 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}+1\&,1\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}+1\&,3\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}+1\&,2\right ]}+1
\]