Internal problem ID [2203]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y=3 \,{\mathrm e}^{-4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+3*y(x)=3*exp(-4*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\sqrt {3}\, x \right ) c_{2} +\cos \left (\sqrt {3}\, x \right ) c_{1} +\frac {3 \,{\mathrm e}^{-4 x}}{19} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
DSolve[y''[x]+3*y[x]==3*Exp[-4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 e^{-4 x}}{19}+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \]