38.2.43 problem 43

Internal problem ID [6472]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 43
Date solved : Sunday, March 30, 2025 at 11:04:48 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+x +x y^{2}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.060 (sec). Leaf size: 14

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

\[ y = -\tan \left (\frac {x^{2}}{2}-\frac {1}{2}\right ) \]

✓ Mathematica. Time used: 0.255 (sec). Leaf size: 17

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

\[ y(x)\to \tan \left (\frac {1}{2} \left (1-x^2\right )\right ) \]

✓ Sympy. Time used: 0.318 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \tan {\left (\frac {x^{2}}{2} - \frac {1}{2} \right )} \]