39.1.10 problem Problem 11.12

Internal problem ID [6515]
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
Date solved : Monday, January 27, 2025 at 02:11:11 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x)-5*y(x)=(x-1)*sin(x)+(x+1)*cos(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{5 x} c_1 +\frac {\left (-78 x -69\right ) \cos \left (x \right )}{338}+\frac {\left (-52 x +71\right ) \sin \left (x \right )}{338} \]

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 36

DSolve[D[y[x],x]-5*y[x]==(x-1)*Sin[x]+(x+1)*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{338} ((71-52 x) \sin (x)-3 (26 x+23) \cos (x))+c_1 e^{5 x} \]