Internal problem ID [5018]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime } \left (y^{\prime }+y\right )-x \left (x +y\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = \frac {x^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 27
DSolve[{y'[x]*(y'[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+\sinh (x)-\cosh (x)+1 \\ \end{align*}