47.2.23 problem 23

Internal problem ID [7439]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:59:31 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

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

\[ y = \frac {x^{2}}{2} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 28

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

\begin{align*} y(x)\to \frac {x^2}{2} \\ y(x)\to -x-e^{-x}+1 \\ \end{align*}