76.15.32 problem 33

Internal problem ID [17673]
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 : 33
Date solved : Tuesday, January 28, 2025 at 10:53:43 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+5*y(x)=x,y(x), singsol=all)
 

\[ y = \frac {x^{6}+3 c_{1} x^{4}-4 c_{1}^{3}+12 c_{2}}{12 x^{5}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+5*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^5}+\frac {x}{12}+\frac {c_2}{x} \]