12.10.26 problem 26

Internal problem ID [1830]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number : 26
Date solved : Monday, January 27, 2025 at 05:36:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=2 x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-2*x*(x+2)*diff(y(x),x)+(x^2+4*x+6)*y(x)=2*x*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} x \left (c_1 \,x^{2}+c_2 x +1\right ) \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]-2*x*(x+2)*D[y[x],x]+(x^2+4*x+6)*y[x]==2*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x x \left (c_2 x^2+c_1 x+1\right ) \]