12.10.29 problem 29

Internal problem ID [1833]
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 : 29
Date solved : Monday, January 27, 2025 at 05:36:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y&=x^{{5}/{2}} {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 21

dsolve(4*x^2*diff(y(x),x$2)-4*x*(x+1)*diff(y(x),x)+(2*x+3)*y(x)=x^(5/2)*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 30

DSolve[4*x^2*D[y[x],{x,2}]-4*x*(x+1)*D[y[x],x]+(2*x+3)*y[x]==x^(5/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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