56.3.14 problem 14
Internal
problem
ID
[8872]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
3.0
Problem
number
:
14
Date
solved
:
Monday, January 27, 2025 at 05:11:24 PM
CAS
classification
:
[[_3rd_order, _with_linear_symmetries]]
\begin{align*} y^{\prime \prime \prime }+y^{\prime }+y&=x \end{align*}
With initial conditions
\begin{align*} y^{\prime }\left (0\right )&=0\\ y \left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1 \end{align*}
✓ Solution by Maple
Time used: 0.631 (sec). Leaf size: 447
dsolve([diff(y(x),x$3)+diff(y(x),x)+y(x)=x,D(y)(0) = 0, y(0) = 0, (D@@2)(y)(0) = 1],y(x), singsol=all)
\[
y = \frac {\frac {10 \,{\mathrm e}^{-\frac {\left (108+12 \sqrt {93}\right )^{{1}/{3}} \left (-12+\left (-9+\sqrt {93}\right ) \left (108+12 \sqrt {93}\right )^{{1}/{3}}\right ) x}{144}} \left (\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} \sqrt {3}\, \sqrt {31}+\frac {3 \sqrt {3}\, \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}} \sqrt {31}}{5}-\frac {6 \sqrt {3}\, \sqrt {31}}{5}-\frac {39 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}}{5}-\frac {31 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}}}{5}+\frac {114}{5}\right ) \cos \left (\frac {\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} \sqrt {3}\, \left (\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} \sqrt {3}\, \sqrt {31}-9 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}+12\right ) x}{144}\right )}{3}-26 \,{\mathrm e}^{-\frac {\left (108+12 \sqrt {93}\right )^{{1}/{3}} \left (-12+\left (-9+\sqrt {93}\right ) \left (108+12 \sqrt {93}\right )^{{1}/{3}}\right ) x}{144}} \left (\left (\sqrt {3}-\frac {5 \sqrt {31}}{13}\right ) \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}+\frac {38 \sqrt {3}}{13}-\frac {6 \sqrt {31}}{13}\right ) \sin \left (\frac {\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} \sqrt {3}\, \left (\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} \sqrt {3}\, \sqrt {31}-9 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}+12\right ) x}{144}\right )+\left (-76-\frac {10 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} \sqrt {3}\, \sqrt {31}}{3}+\sqrt {3}\, \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}} \sqrt {31}+4 \sqrt {3}\, \sqrt {31}+26 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}-\frac {31 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}}}{3}\right ) {\mathrm e}^{\frac {\left (108+12 \sqrt {93}\right )^{{1}/{3}} \left (-12+\left (-9+\sqrt {93}\right ) \left (108+12 \sqrt {93}\right )^{{1}/{3}}\right ) x}{72}}+3 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}} \left (x -1\right ) \left (\sqrt {3}\, \sqrt {31}-\frac {31}{3}\right )}{\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}} \left (3 \sqrt {3}\, \sqrt {31}-31\right )}
\]
✓ Solution by Mathematica
Time used: 0.020 (sec). Leaf size: 1546
DSolve[{D[y[x],{x,3}]+D[y[x],x]+y[x]==x,{Derivative[1][y][1] == 0,y[0]==0,Derivative[2][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
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