Internal problem ID [4664]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page
95
Problem number: Problem 11.12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-5 y-\left (x -1\right ) \sin \relax (x )-\left (1+x \right ) \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 29
dsolve(diff(y(x),x)-5*y(x)=(x-1)*sin(x)+(x+1)*cos(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 x \cos \relax (x )}{13}-\frac {69 \cos \relax (x )}{338}-\frac {2 \sin \relax (x ) x}{13}+\frac {71 \sin \relax (x )}{338}+{\mathrm e}^{5 x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 36
DSolve[y'[x]-5*y[x]==(x-1)*Sin[x]+(x+1)*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{338} ((71-52 x) \sin (x)-3 (26 x+23) \cos (x))+c_1 e^{5 x} \\ \end{align*}