75.25.4 problem 760

Internal problem ID [17227]
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 ODEs). Section 18.3. Finding periodic solutions of linear differential equations. Exercises page 187
Problem number : 760
Date solved : Tuesday, January 28, 2025 at 09:58:06 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\arcsin \left (\sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = {\mathrm e}^{2 x} \left (c_{2} +c_{1} x -\int \arcsin \left (\sin \left (x \right )\right ) x \,{\mathrm e}^{-2 x}d x +x \left (\int \arcsin \left (\sin \left (x \right )\right ) {\mathrm e}^{-2 x}d x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 59

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==ArcSin[Sin[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (x \int _1^xe^{-2 K[2]} \arcsin (\sin (K[2]))dK[2]+\int _1^x-e^{-2 K[1]} \arcsin (\sin (K[1])) K[1]dK[1]+c_2 x+c_1\right ) \]