Internal problem ID [2183]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 10.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }={\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)-5*diff(y(x),x)=exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-5 x} \left (-5 \,{\mathrm e}^{6 x} c_{2} -5 c_{3} {\mathrm e}^{5 x}+c_{1} -\frac {5 \,{\mathrm e}^{8 x}}{48}\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 34
DSolve[y'''[x]+4*y''[x]-5*y'[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{3 x}}{48}-\frac {1}{5} c_1 e^{-5 x}+c_2 e^x+c_3 \]