Internal problem ID [5376]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=\sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-y(x)=sin(x)^2,y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+\frac {\cos \left (x \right )^{2}}{5}-\frac {3}{5} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 30
DSolve[y''[x]-y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{10} (\cos (2 x)-5)+c_1 e^x+c_2 e^{-x} \]