83.14.3 problem 3

Internal problem ID [19182]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (F) at page 42
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:11:40 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{x}+\sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+4*y(x)=exp(x)+sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-x +4 c_{1} \right ) \cos \left (2 x \right )}{4}+\frac {\left (1+8 c_{2} \right ) \sin \left (2 x \right )}{8}+\frac {{\mathrm e}^{x}}{5} \]

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+4*y[x]==Exp[x]+Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{5}+\frac {1}{8} \sin (x) \cos (x)+\left (-\frac {x}{4}+c_1\right ) \cos (2 x)+c_2 \sin (2 x) \]