Internal problem ID [5148]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page
1094
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=2 \cosh \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=2*cosh(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +{\mathrm e}^{-2 x} c_{1} +\frac {\left (-12 x -7\right ) {\mathrm e}^{-2 x}}{36}+\frac {{\mathrm e}^{2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 39
DSolve[y''[x]+y'[x]-2*y[x]==2*Cosh[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{36} e^{-2 x} \left (-12 x+9 e^{4 x}+36 c_2 e^{3 x}-4+36 c_1\right ) \]