81.1.23 problem 2-21

Internal problem ID [21468]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-21
Date solved : Thursday, October 02, 2025 at 07:39:06 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 10

ode:=diff(y(x),x) = 2*x*y(x); 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{x^{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 12

ode=D[y[x],x]==2*x*y[x]; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 e^{x^2} \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 e^{x^{2}} \]