60.3.56 problem 1061

Internal problem ID [11052]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1061
Date solved : Wednesday, March 05, 2025 at 01:39:25 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}}&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)+diff(y(x),x)*x^(1/2)+(1/4/x^(1/2)+1/4*x-9)*y(x)-x*exp(-1/3*x^(3/2)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} \left (-9 \cosh \left (3 x \right ) c_{1} -9 \sinh \left (3 x \right ) c_{2} +x \right )}{9} \]

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 79

ode=-(x/E^(x^(3/2)/3)) + (-9 + 1/(4*Sqrt[x]) + x/4)*y[x] + Sqrt[x]*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{6} e^{-\frac {1}{3} \left (\sqrt {x}+9\right ) x} \left (6 \int _1^x-\frac {1}{6} e^{3 K[1]} K[1]dK[1]+e^{6 x} \int _1^xe^{-3 K[2]} K[2]dK[2]+c_2 e^{6 x}+6 c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(x)*Derivative(y(x), x) - x*exp(-x**(3/2)/3) + (x/4 - 9 + 1/(4*sqrt(x)))*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE sqrt(x)*y(x)/4 - sqrt(x)*exp(-x**(3/2)/3) + Derivative(y(x), x) + y(x)/(4*x) - 9*y(x)/sqrt(x) + Derivative(y(x), (x, 2))/sqrt(x) cannot be solved by the factorable group method