84.17.5 problem 10.6

Internal problem ID [22197]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Solved problems. Page 54
Problem number : 10.6
Date solved : Thursday, October 02, 2025 at 08:34:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }+\left (1+x \right ) y&=0 \end{align*}

With initial conditions

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

ValueError : Couldnt solve for initial conditions