10.2.13 problem 13

Internal problem ID [1141]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:35:33 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 18

dsolve([diff(y(x),x) = 2*x/(y(x)+x^2*y(x)),y(0) = -2],y(x), singsol=all)
 

\[ y = -\sqrt {2 \ln \left (x^{2}+1\right )+4} \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 24

DSolve[{D[y[x],x] == 2*x/(y[x]+x^2*y[x]),y[0]==-2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {2} \sqrt {\log \left (x^2+1\right )+2} \]