Internal problem ID [4254]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+3 x y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x)+3*x*y(x)=1,y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x^{2}}{2}+c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 20
DSolve[x^2*y'[x]+3*x*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2+2 c_1}{2 x^3} \\ \end{align*}