75.20.19 problem 658

Internal problem ID [17153]
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 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 658
Date solved : Tuesday, January 28, 2025 at 09:54:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=1/(exp(x)*sin(x)),y(x), singsol=all)
 

\[ y = -\left (-\ln \left (\sin \left (x \right )\right ) \sin \left (x \right )+\left (x -c_{1} \right ) \cos \left (x \right )-\sin \left (x \right ) c_{2} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+2*y[x]==1/(Exp[x]*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} ((-x+c_2) \cos (x)+\sin (x) (\log (\sin (x))+c_1)) \]