Internal problem ID [6450]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 14.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }+y-x=0} \] 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: 0.625 (sec). Leaf size: 359
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 \left (x \right ) = \frac {\frac {10 \,{\mathrm e}^{-\frac {\left (-12+\left (-9+\sqrt {93}\right ) \left (108+12 \sqrt {93}\right )^{\frac {1}{3}}\right ) \left (108+12 \sqrt {93}\right )^{\frac {1}{3}} x}{144}} \left (\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} \sqrt {3}\, \sqrt {31}+\frac {3 \sqrt {3}\, \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}} \sqrt {31}}{5}-\frac {6 \sqrt {3}\, \sqrt {31}}{5}-\frac {39 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}}{5}-\frac {31 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}}{5}+\frac {114}{5}\right ) \cos \left (\frac {\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} \sqrt {3}\, \left (\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} \sqrt {3}\, \sqrt {31}-9 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+12\right ) x}{144}\right )}{3}-26 \,{\mathrm e}^{-\frac {\left (-12+\left (-9+\sqrt {93}\right ) \left (108+12 \sqrt {93}\right )^{\frac {1}{3}}\right ) \left (108+12 \sqrt {93}\right )^{\frac {1}{3}} x}{144}} \left (\left (\sqrt {3}-\frac {5 \sqrt {31}}{13}\right ) \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+\frac {38 \sqrt {3}}{13}-\frac {6 \sqrt {31}}{13}\right ) \sin \left (\frac {\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} \sqrt {3}\, \left (\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} \sqrt {3}\, \sqrt {31}-9 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+12\right ) x}{144}\right )+\left (-76-\frac {10 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} \sqrt {3}\, \sqrt {31}}{3}+\sqrt {3}\, \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}} \sqrt {31}+4 \sqrt {3}\, \sqrt {31}+26 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}-\frac {31 \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}}{3}\right ) {\mathrm e}^{\frac {\left (-12+\left (-9+\sqrt {93}\right ) \left (108+12 \sqrt {93}\right )^{\frac {1}{3}}\right ) \left (108+12 \sqrt {93}\right )^{\frac {1}{3}} x}{72}}+3 \left (\sqrt {3}\, \sqrt {31}-\frac {31}{3}\right ) \left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}} \left (x -1\right )}{\left (108+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}} \left (3 \sqrt {3}\, \sqrt {31}-31\right )} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 1546
DSolve[{y'''[x]+y'[x]+y[x]==x,{y'[1] == 0,y[0]==0,y''[0]==1}},y[x],x,IncludeSingularSolutions -> True]
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