40.10.6 problem 15

Internal problem ID [6728]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 15. Linear equations with constant coefficients (Variation of parameters). Supplemetary problems. Page 98
Problem number : 15
Date solved : Monday, January 27, 2025 at 02:25:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y&=2+{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

\[ y = \sin \left (\sqrt {2}\, x \right ) c_2 +\cos \left (\sqrt {2}\, x \right ) c_1 +1+\frac {{\mathrm e}^{x}}{3} \]

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 36

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

\[ y(x)\to \frac {e^x}{3}+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right )+1 \]