40.9.9 problem 19

Internal problem ID [6719]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:24:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-y(x)=sin(x)^2,y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{x} c_1 +\frac {\cos \left (x \right )^{2}}{5}-\frac {3}{5} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{10} (\cos (2 x)-5)+c_1 e^x+c_2 e^{-x} \]