8.3.25 problem 26

Internal problem ID [701]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:58:28 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

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

\[ y = -\frac {1}{x^{3}+x^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 17

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

\[ y(x)\to -\frac {1}{x^3+x^2-1} \]