28.2.67 problem 67

Internal problem ID [4510]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 67
Date solved : Monday, January 27, 2025 at 09:22:12 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y&=\frac {5 \ln \left (x \right )}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+5*y(x)=5/x^2*ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {5 \sin \left (2 \ln \left (x \right )\right ) c_{2} x +5 \cos \left (2 \ln \left (x \right )\right ) c_{1} x +5 \ln \left (x \right )+2}{5 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 38

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+5*y[x]==5/x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 \log (x)+5 c_2 x \cos (2 \log (x))+5 c_1 x \sin (2 \log (x))+2}{5 x^2} \]