66.1.23 problem Problem 31

Internal problem ID [13870]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 31
Date solved : Tuesday, January 28, 2025 at 06:06:33 AM
CAS classification : [_Abel]

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

With initial conditions

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

✗ Solution by Maple

dsolve([diff(y(x),x)=x*y(x)^3+x^2,y(0) = 0],y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],x]==x*y[x]^3+x^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved