75.6.20 problem 153

Internal problem ID [16697]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 153
Date solved : Thursday, March 13, 2025 at 08:32:12 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.360 (sec). Leaf size: 11

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

\[ y = {\mathrm e}^{x}+{\mathrm e}^{\frac {1}{x}} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 14

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

\[ y(x)\to e^{\frac {1}{x}}+e^x \]

✓ Sympy. Time used: 1.144 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \left (e^{\frac {1}{inf}} - e^{\frac {1}{inf}} e^{- inf}\right ) e^{\frac {1}{x}} + e^{x} \]