Internal problem ID [4631]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+25 y-5 x^{2}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+25*y(x)=5*x^2+x,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (5 x \right ) c_{2}+\cos \left (5 x \right ) c_{1}+\frac {x^{2}}{5}+\frac {x}{25}-\frac {2}{125} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 34
DSolve[y''[x]+25*y[x]==5*x^2+x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{125} (5 x-1) (5 x+2)+c_1 \cos (5 x)+c_2 \sin (5 x) \\ \end{align*}