56.5.6 problem 6

Internal problem ID [8967]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:25:33 PM
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: 0.006 (sec). Leaf size: 19

dsolve(x*diff(diff(y(x),x),x)-(2*x+2)*diff(y(x),x)+(2+x)*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: 0.064 (sec). Leaf size: 31

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

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