62.36.2 problem Ex 2

Internal problem ID [13000]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60. Exact equation. Integrating factor. Page 139
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:47:12 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 26

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

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