Internal problem ID [15375]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 606.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y=2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 25
dsolve([diff(y(x),x$3)-y(x)=2*x,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -2 x +\frac {4 \,{\mathrm e}^{x}}{3}-\frac {4 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {x \sqrt {3}}{2}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 38
DSolve[{y'''[x]-y[x]==2*x,{y[0]==0,y'[0]==0,y''[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (-6 x+4 e^x-4 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )\right ) \]