23.5.118 problem 118

Internal problem ID [6727]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 118
Date solved : Tuesday, September 30, 2025 at 03:51:11 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 x y+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=10 x^{2}+10 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 41

ode:=2*x*y(x)+2*x^3*diff(diff(y(x),x),x)+x^4*diff(diff(diff(y(x),x),x),x) = 10*x^2+10; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 c_3 \,x^{2} \sin \left (\ln \left (x \right )\right )+5 c_2 \,x^{2} \cos \left (\ln \left (x \right )\right )+25 x^{2}+10 \ln \left (x \right )+5 c_1 +8}{5 x} \]

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 42

ode=2*x*y[x] + 2*x^3*D[y[x],{x,2}] + x^4*D[y[x],{x,3}] == 10*(1 + x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {25 x^2+10 \log (x)+8+5 c_3}{5 x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \end{align*}

✓ Sympy. Time used: 0.284 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 3)) + 2*x**3*Derivative(y(x), (x, 2)) - 10*x**2 + 2*x*y(x) - 10,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x^{2} \left (C_{2} \sin {\left (\log {\left (x \right )} \right )} + C_{3} \cos {\left (\log {\left (x \right )} \right )} + 5\right ) + 2 \log {\left (x \right )}}{x} \]