Internal problem ID [4640]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }+10 y-20+{\mathrm e}^{2 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)-diff(y(x),x)+10*y(x)=20-exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {39}\, x}{2}\right ) c_{2} +{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {39}\, x}{2}\right ) c_{1} +2-\frac {{\mathrm e}^{2 x}}{12} \]
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 53
DSolve[y''[x]-y'[x]+10*y[x]==20-Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{2 x}}{12}+e^{x/2} \left (c_2 \cos \left (\frac {\sqrt {39} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {39} x}{2}\right )\right )+2 \\ \end{align*}