15.12.24 problem 24

Internal problem ID [3168]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 24
Date solved : Monday, January 27, 2025 at 07:24:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

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

\[ y = \frac {\left (\ln \left (x \right ) x^{2}-\frac {3 x^{2}}{2}+8 c_{1} x +8 c_2 \right ) {\mathrm e}^{\frac {x}{2}}}{8} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 38

DSolve[4*D[y[x],{x,2}]-4*D[y[x],x]+y[x]==Exp[x/2]*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{x/2} \left (-3 x^2+2 x^2 \log (x)+16 c_2 x+16 c_1\right ) \]