Internal problem ID [15028]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 126.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {-y^{\prime } x -y=-x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([x^2-x*diff(y(x),x)=y(x),y(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}-1}{3 x} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 17
DSolve[{x^2-x*y'[x]==y[x],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3-1}{3 x} \]