21.6 problem 2(a)

Internal problem ID [5315]

Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }-y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \left (x_{0}\right ) = y_{0}] \end {align*}

Solution by Maple

Time used: 0.044 (sec). Leaf size: 18

dsolve([diff(y(x),x)=y(x)^2,y(x__0) = y__0],y(x), singsol=all)
 

\[ y \relax (x ) = -\frac {y_{0}}{-1+\left (x -x_{0}\right ) y_{0}} \]

Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 16

DSolve[{y'[x]==x2*y[x],{y[x0]==y0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {y0} e^{\text {x2} (x-\text {x0})} \\ \end{align*}