39.2.8 problem Problem 11.51

Internal problem ID [6525]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.51
Date solved : Monday, January 27, 2025 at 02:11:30 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 29

dsolve(diff(y(x),x)-y(x)=sin(x)+cos(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 37

DSolve[D[y[x],x]-y[x]==Sin[x]+Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{10} \left (-5 \sin (x)+4 \sin (2 x)-5 \cos (x)-2 \cos (2 x)+10 c_1 e^x\right ) \]