Internal problem ID [15423]
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 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 658.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\left (-\ln \left (\sin \left (x \right )\right ) \sin \left (x \right )+\left (x -c_{1} \right ) \cos \left (x \right )-\sin \left (x \right ) c_{2} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 30
DSolve[y''[x]+2*y'[x]+2*y[x]==1/(Exp[x]*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} ((-x+c_2) \cos (x)+\sin (x) (\log (\sin (x))+c_1)) \]