Internal problem ID [13793]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.3 (a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=30 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)-4*diff(y(x),x)=30*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-4 \,{\mathrm e}^{5 x}-c_{2} {\mathrm e}^{4 x}-2 c_{3} {\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 37
DSolve[y'''[x]-4*y'[x]==30*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{3 x}+\frac {1}{2} c_1 e^{2 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]