Internal problem ID [2222]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 21.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+diff(y(x),x$2)=x^2,y(x), singsol=all)
\[ y = \frac {x^{4}}{12}+3 x^{2}+\frac {2 x^{3}}{3}+c_{1} \left (x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{x}\right )+c_{2} {\mathrm e}^{x}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 46
DSolve[y''''[x]-2*y'''[x]+y''[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{12}+\frac {2 x^3}{3}+3 x^2+c_4 x+c_1 e^x+c_2 e^x (x-2)+c_3 \]