12.10.15 problem 15

Internal problem ID [1819]
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 : 15
Date solved : Monday, January 27, 2025 at 05:36:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=6 x^{3} {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve(x*diff(y(x),x$2)-(2*x+2)*diff(y(x),x)+(x+2)*y(x)=6*x^3*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_2 +c_1 \,x^{3}+\frac {3}{2} x^{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 29

DSolve[x*D[y[x],{x,2}]-(2*x+2)*D[y[x],x]+(x+2)*y[x]==6*x^3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^x \left (9 x^4+2 c_2 x^3+6 c_1\right ) \]