Internal problem ID [11853]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y=\sin \left (x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(sin(x)^2*diff(y(x),x$2)-2*sin(x)*cos(x)*diff(y(x),x)+(cos(x)^2+1)*y(x)=sin(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) \left (c_{2} +c_{1} x +\frac {1}{2} x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 24
DSolve[Sin[x]^2*y''[x]-2*Sin[x]*Cos[x]*y'[x]+(Cos[x]^2+1)*y[x]==Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x^2+2 c_2 x+2 c_1\right ) \sin (x) \]