Internal problem ID [5147]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=4 \sinh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=4*sinh(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-2 x^{2}+\left (2 c_{1} +2\right ) x +2 c_{2} +1\right ) {\mathrm e}^{-x}}{2}+\frac {{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 31
DSolve[y''[x]+2*y'[x]+y[x]==4*Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{2}+e^{-x} \left (-x^2+c_2 x+c_1\right ) \]