60.3.247 problem 1263

Internal problem ID [11243]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1263
Date solved : Sunday, March 30, 2025 at 07:58:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 47

ode:=x*(x+3)*diff(diff(y(x),x),x)+(3*x-1)*diff(y(x),x)+y(x)-(20*x+30)*(x^2+3*x)^(7/3) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (c_2 +\int \frac {3 \left (x +3\right )^{{4}/{3}} \left (x^{3} \left (x +3\right )^{3} \left (x \left (x +3\right )\right )^{{1}/{3}}+\frac {c_1}{3}\right )}{x^{{7}/{3}}}d x \right ) x^{{4}/{3}}}{\left (x +3\right )^{{7}/{3}}} \]

✓ Mathematica. Time used: 1.023 (sec). Leaf size: 328

ode=(-30 - 20*x)*(3*x + x^2)^(7/3) + y[x] + (-1 + 3*x)*D[y[x],x] + x*(3 + x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]+7}{2 K[1]^2+6 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {3 K[2]-1}{K[2] (K[2]+3)}dK[2]\right ) \left (\int _1^x-10 \exp \left (\int _1^{K[4]}\frac {K[1]+7}{2 K[1]^2+6 K[1]}dK[1]+\frac {1}{2} \int _1^{K[4]}\frac {3 K[2]-1}{K[2] (K[2]+3)}dK[2]\right ) K[4] \sqrt [3]{K[4] (K[4]+3)} \left (2 K[4]^2+9 K[4]+9\right ) \int _1^{K[4]}\exp \left (-2 \int _1^{K[3]}\frac {K[1]+7}{2 K[1]^2+6 K[1]}dK[1]\right )dK[3]dK[4]+\int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]+7}{2 K[1]^2+6 K[1]}dK[1]\right )dK[3] \left (\int _1^x10 \exp \left (\int _1^{K[5]}\frac {K[1]+7}{2 K[1]^2+6 K[1]}dK[1]+\frac {1}{2} \int _1^{K[5]}\frac {3 K[2]-1}{K[2] (K[2]+3)}dK[2]\right ) K[5] \sqrt [3]{K[5] (K[5]+3)} \left (2 K[5]^2+9 K[5]+9\right )dK[5]+c_2\right )+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x + 3)*Derivative(y(x), (x, 2)) + (3*x - 1)*Derivative(y(x), x) - (20*x + 30)*(x**2 + 3*x)**(7/3) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (20*x**5*(x*(x + 3))**(1/3) + 150*x**4*(x*(x + 3))**(1/3) + 360*x**3*(x*(x + 3))**(1/3) + 270*x**2*(x*(x + 3))**(1/3) - x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), (x, 2)) - y(x))/(3*x - 1) cannot be solved by the factorable group method