38.3.4 problem 4

Internal problem ID [6482]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 4
Date solved : Monday, January 27, 2025 at 02:07:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+25 y&=5 x^{2}+x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+25*y(x)=5*x^2+x,y(x), singsol=all)
 

\[ y = \sin \left (5 x \right ) c_2 +\cos \left (5 x \right ) c_1 +\frac {x^{2}}{5}+\frac {x}{25}-\frac {2}{125} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+25*y[x]==5*x^2+x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{125} \left (25 x^2+5 x-2\right )+c_1 \cos (5 x)+c_2 \sin (5 x) \]