76.1.19 problem 19

Internal problem ID [17318]
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 : 19
Date solved : Tuesday, January 28, 2025 at 09:59:54 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 20

dsolve([diff(y(x),x)=2*x*y(x)^2+4*x^3*y(x)^2,y(1) = -2],y(x), singsol=all)
 

\[ y = -\frac {2}{2 x^{4}+2 x^{2}-3} \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 21

DSolve[{D[y[x],x]==2*x*y[x]^2+4*x^3*y[x]^2,{y[1]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2}{2 x^4+2 x^2-3} \]