34.14.8 problem 29

Internal problem ID [8065]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 29
Date solved : Friday, October 03, 2025 at 02:13:03 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=8 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 19

ode:=(2*x-3)*diff(diff(diff(y(x),x),x),x)-(6*x-7)*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-4*y(x) = 8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -2+c_1 x +c_2 \,{\mathrm e}^{x}+c_3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 219

ode=(2*x-3)*D[y[x],{x,3}]-(6*x-7)*D[y[x],{x,2}]+4*x*D[y[x],x]-4*y[x]==8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x \int _1^x\exp \left (\int _1^{K[4]}\left (-\frac {1}{2 K[1]}-\frac {1}{2}+\frac {1}{3-2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^{K[4]}\left (\frac {3}{K[2]}-3+\frac {2}{3-2 K[2]}\right )dK[2]\right ) (K[4]-1)dK[4]+c_3 x \int _1^x\exp \left (\int _1^{K[5]}\left (-\frac {1}{2 K[1]}-\frac {1}{2}+\frac {1}{3-2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^{K[5]}\left (\frac {3}{K[2]}-3+\frac {2}{3-2 K[2]}\right )dK[2]\right ) (K[5]-1) \int _1^{K[5]}\frac {\exp \left (-2 \int _1^{K[3]}-\frac {-2 K[1]^2-K[1]+3}{6 K[1]-4 K[1]^2}dK[1]\right )}{(K[3]-1)^2}dK[3]dK[5]+c_1 x-2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x) + (2*x - 3)*Derivative(y(x), (x, 3)) - (6*x - 7)*Derivative(y(x), (x, 2)) - 4*y(x) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (2*x*(3*Derivative(y(x), (x, 2)) - Derivative(y(x), (x, 3))) + 4*y(x) - 7*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)) + 8)/(4*x) cannot be solved by the factorable group method