85.2.7 problem 6

Internal problem ID [22434]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. B Exercises at page 14
Problem number : 6
Date solved : Thursday, October 02, 2025 at 08:39:20 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+2 y x \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 20

ode:=diff(y(x),x) = 1+2*x*y(x); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\sqrt {\pi }\, \left (-\operatorname {erf}\left (x \right )+\operatorname {erf}\left (1\right )\right ) {\mathrm e}^{x^{2}}}{2} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 26

ode=D[y[x],{x,1}]==1+2*x*y[x]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \sqrt {\pi } e^{x^2} (\text {erf}(x)-\text {erf}(1)) \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + Derivative(y(x), x) - 1,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {\sqrt {\pi } \operatorname {erf}{\left (x \right )}}{2} - \frac {\sqrt {\pi } \operatorname {erf}{\left (1 \right )}}{2}\right ) e^{x^{2}} \]