Internal problem ID [2140]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=3 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-4*y(x)=3*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{1} -\frac {3 \cos \left (x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 28
DSolve[y''[x]-4*y[x]==3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3 \cos (x)}{5}+c_1 e^{2 x}+c_2 e^{-2 x} \]