83.27.10 problem 10

Internal problem ID [19285]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 10
Date solved : Monday, March 31, 2025 at 07:05:39 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y&=\left (1+x \right ) {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=(2*x^2+3*x)*diff(diff(y(x),x),x)+(3+6*x)*diff(y(x),x)+2*y(x) = (1+x)*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 +c_1 \ln \left (x \right )+{\mathrm e}^{x}}{2 x +3} \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 24

ode=(2*x^2+3*x)*D[y[x],{x,2}]+(6*x+3)*D[y[x],x]+2*y[x]==(1+x)*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^x+c_2 \log (x)+c_1}{2 x+3} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - 1)*exp(x) + (6*x + 3)*Derivative(y(x), x) + (2*x**2 + 3*x)*Derivative(y(x), (x, 2)) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-2*x**2*Derivative(y(x), (x, 2)) + x*exp(x) - 3*x*Derivative(y(x), (x, 2)) - 2*y(x) + exp(x))/(3*(2*x + 1)) cannot be solved by the factorable group method