Internal problem ID [2164]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=8 \sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+4*y(x)=8*sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} -1\right ) \cos \left (2 x \right )+1+\left (c_{2} -x \right ) \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 27
DSolve[y''[x]+4*y[x]==8*Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (-1+c_1) \cos (2 x)+(-x+c_2) \sin (2 x)+1 \]