Internal problem ID [11843]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\frac {1}{1+\sin \left (x \right )}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+y(x)=1/(1+sin(x)),y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (1+\sin \left (x \right )\right ) \sin \left (x \right )+\left (-x +c_{1} -1\right ) \cos \left (x \right )-1+\left (c_{2} +1\right ) \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 40
DSolve[y''[x]+y[x]==1/(1+Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (-x+1+c_1) \cos (x)+\sin (x) \left (2 \log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+1+c_2\right )-1 \]