83.26.22 problem 22

Internal problem ID [19275]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 22
Date solved : Monday, March 31, 2025 at 07:05:19 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }&=\left (2 x +3\right ) \left (2 x +4\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=(1+x)^2*diff(diff(y(x),x),x)+(1+x)*diff(y(x),x) = (2*x+3)*(2*x+4); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (x +1\right )^{2}+\left (c_1 -8\right ) \ln \left (x +1\right )+x^{2}+8 x +c_2 +7 \]

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 29

ode=(x+1)^2*D[y[x],{x,2}]+(x+1)*D[y[x],x]==(2*x+3)*(2*x+4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2+8 x+\frac {1}{4} (2 \log (x+1)+c_1){}^2+c_2 \]

✓ Sympy. Time used: 0.580 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)**2*Derivative(y(x), (x, 2)) + (x + 1)*Derivative(y(x), x) - (2*x + 3)*(2*x + 4),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \log {\left (x + 1 \right )} + x^{2} + 8 x + \log {\left (x + 1 \right )}^{2} \]