15.11.31 problem 31

Internal problem ID [3141]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 31
Date solved : Monday, January 27, 2025 at 07:23:20 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} 2 y^{\prime \prime }+y^{\prime }&=8 \sin \left (2 x \right )+{\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 28

dsolve([2*diff(y(x),x$2)+diff(y(x),x)=8*sin(2*x)+exp(-x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {98 \,{\mathrm e}^{-\frac {x}{2}}}{17}-\frac {16 \sin \left (2 x \right )}{17}+{\mathrm e}^{-x}-\frac {4 \cos \left (2 x \right )}{17}+6 \]

✓ Solution by Mathematica

Time used: 0.419 (sec). Leaf size: 39

DSolve[{2*D[y[x],{x,2}]+D[y[x],x]==8*Sin[2*x]+Exp[-x],{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x}-\frac {98 e^{-x/2}}{17}-\frac {16}{17} \sin (2 x)-\frac {4}{17} \cos (2 x)+6 \]