64.12.16 problem 16

Internal problem ID [13520]
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 : 16
Date solved : Tuesday, January 28, 2025 at 05:51:42 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)*arcsin(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x} \left (2 x^{2} \arcsin \left (x \right )+3 \sqrt {-x^{2}+1}\, x +4 c_{1} x +\arcsin \left (x \right )+4 c_{2} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 45

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==Exp[x]*ArcSin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^x \left (2 x^2 \arcsin (x)+\arcsin (x)+3 \sqrt {1-x^2} x+4 c_2 x+4 c_1\right ) \]