Internal problem ID [11844]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y={\mathrm e}^{x} \arcsin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (2 x^{2} \arcsin \left (x \right )+3 x \sqrt {-x^{2}+1}+4 c_{1} x +\arcsin \left (x \right )+4 c_{2} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 45
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]*ArcSin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^x \left (2 x^2 \arcsin (x)+\arcsin (x)+3 \sqrt {1-x^2} x+4 c_2 x+4 c_1\right ) \]