Internal problem ID [15497]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.3. Finding periodic solutions of linear
differential equations. Exercises page 187
Problem number: 760.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=\arcsin \left (\sin \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=arcsin(sin(x)),y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \left (c_{2} +c_{1} x -\left (\int \arcsin \left (\sin \left (x \right )\right ) x \,{\mathrm e}^{-2 x}d x \right )+x \left (\int \arcsin \left (\sin \left (x \right )\right ) {\mathrm e}^{-2 x}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 1.363 (sec). Leaf size: 38
DSolve[y''[x]-4*y'[x]+4*y[x]==ArcSin[Sin[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (\arcsin (\sin (x))+4 e^{2 x} (c_2 x+c_1)+\sqrt {\cos ^2(x)} \sec (x)\right ) \]