Internal problem ID [10310]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+3 y^{\prime } x +y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = \frac {c_{2}}{x}+\frac {x}{4}+\frac {c_{1} \ln \relax (x )}{x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 26
DSolve[x^2*y''[x]+3*x*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+4 c_2 \log (x)+4 c_1}{4 x} \\ \end{align*}