49.21.6 problem 2(a)

Internal problem ID [7736]
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)
Date solved : Monday, January 27, 2025 at 03:11:04 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 16

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

\[ y(x)\to \text {y0} e^{\text {x2} (x-\text {x0})} \]