38.4.15 problem 16

Internal problem ID [6501]
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
Date solved : Monday, January 27, 2025 at 02:09:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=50 x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+10*y(x)=50*x,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-3 x} \sin \left (x \right ) c_2 +{\mathrm e}^{-3 x} \cos \left (x \right ) c_1 +5 x -3 \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+10*y[x]==50*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 x+c_2 e^{-3 x} \cos (x)+c_1 e^{-3 x} \sin (x)-3 \]