Internal problem ID [2153]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 14.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }=x^{2}+8} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)=x^2+8,y(x), singsol=all)
\[ y = -\frac {65 x^{2}}{64}-\frac {x^{3}}{48}-\frac {x^{4}}{48}+\frac {{\mathrm e}^{4 x} c_{1}}{16}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 41
DSolve[y'''[x]-4*y''[x]==x^2+8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{192} \left (-4 x^4-4 x^3-195 x^2+12 c_1 e^{4 x}\right )+c_3 x+c_2 \]