Internal problem ID [2224]
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: 23.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }={\mathrm e}^{2 x} \left (x -3\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)=exp(2*x)*(x-3),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-2 x +7\right ) {\mathrm e}^{2 x}}{16}+c_{2} x +\frac {{\mathrm e}^{4 x} c_{1}}{16}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 34
DSolve[y'''[x]-4*y''[x]==Exp[2*x]*(x-3),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} e^{2 x} \left (-2 x+c_1 e^{2 x}+7\right )+c_3 x+c_2 \]