75.4.33 problem 98

Internal problem ID [16664]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 98
Date solved : Monday, March 31, 2025 at 03:04:11 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x \left (\pi +y\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x) = 2*x*(Pi+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\pi +{\mathrm e}^{x^{2}} c_1 \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 24

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

\begin{align*} y(x)\to -\pi +c_1 e^{x^2} \\ y(x)\to -\pi \\ \end{align*}

✓ Sympy. Time used: 0.244 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} e^{x^{2}} - \pi \]