Internal problem ID [13511]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.6 (e).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 10, y^{\prime }\left (0\right ) = 5, y^{\prime \prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([diff(y(x),x$3)=diff(y(x),x$2),y(0) = 10, D(y)(0) = 5, (D@@2)(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = 8+3 x +2 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 15
DSolve[{y'''[x]==y''[x],{y[0]==10,y'[0]==5,y''[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x+2 e^x+8 \]