Internal problem ID [488]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1-2 x}{y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([diff(y(x),x) = (1-2*x)/y(x),y(1) = -2],y(x), singsol=all)
\[ y \relax (x ) = -\sqrt {-2 x^{2}+2 x +4} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 24
DSolve[{y'[x] == (1-2*x)/y[x],y[1]==-2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {-x^2+x+2} \\ \end{align*}