Internal problem ID [5372]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page
92
Problem number: 15.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x$3)-4*diff(y(x),x)=x,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{2}}{8}+\frac {c_{2} {\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{-2 x} c_{1}}{2}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 37
DSolve[y'''[x]-4*y'[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^2}{8}+\frac {1}{2} c_1 e^{2 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]