Internal problem ID [14953]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 2. The method of isoclines. Exercises page 27
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\left (y-1\right ) x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(diff(y(x),x)=(y(x)-1)*x,y(x), singsol=all)
\[ y \left (x \right ) = 1+c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 24
DSolve[y'[x]==(y[x]-1)*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 e^{\frac {x^2}{2}} \\ y(x)\to 1 \\ \end{align*}