64.12.25 problem 25

Internal problem ID [13529]
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
Date solved : Tuesday, January 28, 2025 at 05:52:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \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} \end{align*}

✓ Solution by Maple

Time used: 0.013 (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)
 

\[ y = \sin \left (x \right ) \left (c_{2} +c_{1} x +\frac {1}{2} x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 24

DSolve[Sin[x]^2*D[y[x],{x,2}]-2*Sin[x]*Cos[x]*D[y[x],x]+(Cos[x]^2+1)*y[x]==Sin[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (x^2+2 c_2 x+2 c_1\right ) \sin (x) \]