56.3.30 problem 30

Internal problem ID [8888]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 30
Date solved : Monday, January 27, 2025 at 05:18:36 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 x^{2} y^{\prime \prime }+y&=8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

dsolve(4*x^2*diff(y(x),x$2)+ y(x) = 8*sqrt(x)*(1+ln(x)),y(x), singsol=all)
 

\[ y = \left (c_{2} +c_{1} \ln \left (x \right )+\frac {\ln \left (x \right )^{3}}{3}+\ln \left (x \right )^{2}\right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 37

DSolve[4*x^2*D[y[x],{x,2}]+y[x] == 8*Sqrt[x]*(1+Log[x]),y[x],x,IncludeSingularSolutions -> True]
 

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