Internal problem ID [5389]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }=x^{2}+4 x +8} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+2*diff(y(x),x)=x^2+4*x+8,y(x), singsol=all)
\[ y = \frac {x^{2}}{4}+\frac {x^{3}}{6}+\frac {c_{1} {\mathrm e}^{-2 x}}{2}-c_{2} {\mathrm e}^{-x}+\frac {11 x}{4}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 47
DSolve[y'''[x]+3*y''[x]+2*y'[x]==x^2+4*x+8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{6}+\frac {x^2}{4}+\frac {11 x}{4}-\frac {1}{2} c_1 e^{-2 x}-c_2 e^{-x}+c_3 \]