76.15.31 problem 32

Internal problem ID [17672]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 10:53:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=ln(x),y(x), singsol=all)
 

\[ y = c_{2} x^{2}+c_{1} x^{2} \ln \left (x \right )+\frac {\ln \left (x \right )}{4}+\frac {1}{4} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 29

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (4 c_1 x^2+8 c_2 x^2 \log (x)+\log (x)+1\right ) \]