Internal problem ID [5151]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=x +{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=x+exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +{\mathrm e}^{3 x} c_{1} -{\mathrm e}^{2 x}+\frac {x}{3}+\frac {4}{9} \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 35
DSolve[y''[x]-4*y'[x]+3*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x}{3}-e^{2 x}+c_1 e^x+c_2 e^{3 x}+\frac {4}{9} \]