15.16.8 problem 8

Internal problem ID [3228]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:26:49 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = \frac {c_2}{x}-\frac {x}{4}+1+\frac {\ln \left (x \right ) c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 26

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

\[ y(x)\to -\frac {x}{4}+\frac {c_1}{x}+\frac {c_2 \log (x)}{x}+1 \]