Internal problem ID [4650]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+10 y-50 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+10*y(x)=50*x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-3 x} \sin \relax (x ) c_{2}+{\mathrm e}^{-3 x} \cos \relax (x ) c_{1}+5 x -3 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 27
DSolve[y''[x]+6*y'[x]+10*y[x]==50*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 5 x+e^{-3 x} (c_2 \cos (x)+c_1 \sin (x))-3 \\ \end{align*}