71.1.33 problem 50 (page 56)

Internal problem ID [19209]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 50 (page 56)
Date solved : Thursday, October 02, 2025 at 03:43:45 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(y(x),x) = k*y(x)+f(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\int f \left (x \right ) {\mathrm e}^{-k x}d x +c_1 \right ) {\mathrm e}^{k x} \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 32

ode=D[y[x],x]==k*y[x]+f[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{k x} \left (\int _1^xe^{-k K[1]} f(K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.409 (sec). Leaf size: 24

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

\[ - k \int y{\left (x \right )} e^{- k x}\, dx - \int f{\left (x \right )} e^{- k x}\, dx = C_{1} \]