Internal problem ID [223]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y=\sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2} +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +\frac {3 \cos \left (2 x \right )}{26}-\frac {\sin \left (2 x \right )}{13}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 1.827 (sec). Leaf size: 67
DSolve[y''[x]+y'[x]+y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{13} \sin (2 x)+\frac {3}{26} \cos (2 x)+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+\frac {1}{2} \]