Internal problem ID [5432]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 25.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$3)+diff(y(x),x$2)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{4}}{12}+x^{2}-\frac {x^{3}}{3}+c_{1} {\mathrm e}^{-x}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 37
DSolve[y'''[x]+y''[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{12}-\frac {x^3}{3}+x^2+c_3 x+c_1 e^{-x}+c_2 \]