40.13.10 problem 30

Internal problem ID [6764]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:27:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1+x}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(x^4*diff(y(x),x$2)+2*x^3*diff(y(x),x)+y(x)=(1+x)/x,y(x), singsol=all)
 

\[ y = \sin \left (\frac {1}{x}\right ) c_2 +\cos \left (\frac {1}{x}\right ) c_1 +\frac {x +1}{x} \]

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 25

DSolve[x^4*D[y[x],{x,2}]+2*x^3*D[y[x],x]+y[x]==(1+x)/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x}+c_1 \cos \left (\frac {1}{x}\right )-c_2 \sin \left (\frac {1}{x}\right )+1 \]