33.2.8 problem Problem 11.51

Internal problem ID [7812]
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 : Tuesday, September 30, 2025 at 05:05:49 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 35

ode=D[y[x],x]-y[x]==Sin[x]+Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x \left (\int _1^xe^{-K[1]} (\cos (2 K[1])+\sin (K[1]))dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - sin(x) - cos(2*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} - \frac {\sin {\left (x \right )}}{2} + \frac {2 \sin {\left (2 x \right )}}{5} - \frac {\cos {\left (x \right )}}{2} - \frac {\cos {\left (2 x \right )}}{5} \]