77.48.5 problem Ex 5 page 99

Internal problem ID [20881]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 5 page 99
Date solved : Thursday, October 02, 2025 at 06:43:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3+7 x \right ) y^{\prime }-3 y&=x^{2} \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 28

ode:=2*x^2*(1+x)*diff(diff(y(x),x),x)+x*(7*x+3)*diff(y(x),x)-3*y(x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {7 c_2 \,x^{{5}/{2}}+x^{{7}/{2}}+7 c_1}{x^{{3}/{2}} \left (7 x +7\right )} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 33

ode=2*x^2*(x+1)*D[y[x],{x,2}]+x*(7*x+3)*D[y[x],x]-3*y[x]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\frac {35 c_1}{x^{3/2}}+5 x^2+14 c_2 x}{35 x+35} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*(x + 1)*Derivative(y(x), (x, 2)) - x**2 + x*(7*x + 3)*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-2*x**3*Derivative(y(x), (x, 2)) - 2*x**2*Derivative(y(x), (x, 2)) + x**2 + 3*y(x))/(x*(7*x + 3)) cannot be solved by the factorable group method