Internal problem ID [13501]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 23.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }=8} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 67
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)=8,y(x), singsol=all)
\[ y = \frac {{\mathrm e}^{3 x} \cos \left (\sqrt {3}\, x \right ) c_{1}}{4}+\frac {c_{1} \sqrt {3}\, {\mathrm e}^{3 x} \sin \left (\sqrt {3}\, x \right )}{12}-\frac {c_{2} \sqrt {3}\, {\mathrm e}^{3 x} \cos \left (\sqrt {3}\, x \right )}{12}+\frac {{\mathrm e}^{3 x} \sin \left (\sqrt {3}\, x \right ) c_{2}}{4}+\frac {2 x}{3}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.312 (sec). Leaf size: 71
DSolve[y'''[x]-6*y''[x]+12*y'[x]==8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} \left (8 x-\left (\sqrt {3} c_1-3 c_2\right ) e^{3 x} \cos \left (\sqrt {3} x\right )+\left (3 c_1+\sqrt {3} c_2\right ) e^{3 x} \sin \left (\sqrt {3} x\right )\right )+c_3 \]