74.15.40 problem 40

Internal problem ID [16479]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 09:09:00 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 20

dsolve([x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=ln(x),y(1) = 2, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = -\frac {9}{4 x^{2}}+\frac {5}{x}+\frac {\ln \left (x \right )}{2}-\frac {3}{4} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 25

DSolve[{x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+2*y[x]==Log[x],{y[1]==2,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (-\frac {9}{x^2}+\frac {20}{x}+2 \log (x)-3\right ) \]