Internal problem ID [12466]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (2 y \left (0\right ) \cos \left (2 x \right )+\left (-y \left (0\right )+D\left (y \right )\left (0\right )\right ) \sin \left (2 x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 24
DSolve[y''[x]-2*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (c_2 \cos (2 x)+c_1 \sin (2 x)) \]