76.1.31 problem 31

Internal problem ID [17330]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 10:01:16 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 16

dsolve([diff(y(x),x)=2*y(x)^2+x*y(x)^2,y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 17

DSolve[{D[y[x],x]==2*y[x]^2+x*y[x]^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2}{x^2+4 x-2} \]