Internal problem ID [15373]
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: 604.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime }=-2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(x),x$3)-diff(y(x),x)=-2*x,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x}}{2}+\frac {{\mathrm e}^{x}}{2}+x^{2} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 25
DSolve[{y'''[x]-y'[x]==-2*x,{y[0]==0,y'[0]==1,y''[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2-\frac {e^{-x}}{2}+\frac {e^x}{2} \]