71.1.117 problem 143 (page 213)

Internal problem ID [19293]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 143 (page 213)
Date solved : Thursday, October 02, 2025 at 04:18:28 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

ode:=diff(diff(y(x),x),x)+p__1*diff(y(x),x)+p__2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x \sqrt {p_{1}^{2}-4 p_{2}}}+c_2 \right ) {\mathrm e}^{-\frac {\left (p_{1} +\sqrt {p_{1}^{2}-4 p_{2}}\right ) x}{2}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 47

ode=D[y[x],{x,2}]+p1*D[y[x],x]+p2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\frac {1}{2} x \left (\sqrt {\text {p1}^2-4 \text {p2}}+\text {p1}\right )} \left (c_2 e^{x \sqrt {\text {p1}^2-4 \text {p2}}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.137 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
p__1 = symbols("p__1") 
p__2 = symbols("p__2") 
y = Function("y") 
ode = Eq(p__1*Derivative(y(x), x) + p__2*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (- p^{1} + \sqrt {\left (p^{1}\right )^{2} - 4 p^{2}}\right )}{2}} + C_{2} e^{- \frac {x \left (p^{1} + \sqrt {\left (p^{1}\right )^{2} - 4 p^{2}}\right )}{2}} \]