10.2.10 problem 10

Internal problem ID [1138]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:35:22 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1-2 x}{y} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 18

dsolve([diff(y(x),x) = (1-2*x)/y(x),y(1) = -2],y(x), singsol=all)
 

\[ y = -\sqrt {-2 x^{2}+2 x +4} \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 24

DSolve[{D[y[x],x] == (1-2*x)/y[x],y[1]==-2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {2} \sqrt {-x^2+x+2} \]